Wikibuku idwikibooks https://id.wikibooks.org/wiki/Halaman_Utama MediaWiki 1.45.0-wmf.8 first-letter Media Istimewa Pembicaraan Pengguna Pembicaraan Pengguna Wikibuku Pembicaraan Wikibuku Berkas Pembicaraan Berkas MediaWiki Pembicaraan MediaWiki Templat Pembicaraan Templat Bantuan Pembicaraan Bantuan Kategori Pembicaraan Kategori Resep Pembicaraan Resep Wisata Pembicaraan Wisata TimedText TimedText talk Modul Pembicaraan Modul Soal-Soal Matematika/Eksponen dan logaritma 0 7607 108328 100063 2025-07-07T09:56:14Z Akuindo 8654 108328 wikitext text/x-wiki == Bentuk dan sifat eksponen == bentuk: a<sup>b</sup> = c sifat: #a<sup>m</sup>xa<sup>n</sup> = a<sup>m+n</sup> #a<sup>m</sup>:a<sup>n</sup> = a<sup>m-n</sup> #(a<sup>m</sup>)<sup>n</sup> = a<sup>mxn</sup> #<math>\sqrt[n]{a^m}</math> = a<sup>m/n</sup> #a<sup>m</sup>xb<sup>m</sup> = (axb)<sup>m</sup> #a<sup>m</sup>:b<sup>m</sup> = (a:b)<sup>m</sup> #a<sup>-m</sup> = <math>\frac{1}{a^m}</math> #a<sup>m<sup>n</sup></sup> = a<sup>(m<sup>n</sup>)</sup> #(a<sup>m</sup>)<sup>n</sup> ≠ a<sup>m<sup>n</sup></sup> #0<sup>a</sup> = 0 dengan a > 0 #a<sup>0</sup> = 1 dengan a ≠ 0 #0:a = 0 dengan a ≠ 0 #a<sup>1</sup> = a #a<sup>-1</sup> = <math>\frac{1}{a}</math> dengan a ≠ 0 #a<sup>a</sup> = b<sup>b</sup> dimana a = b ; Tambahan : x<sup>x<sup>……</sup><sup>n</sup></sup> = n maka <math>x = \sqrt[n]{n}</math> dengan x ≥ 1 : x<sup>x<sup>n</sup></sup> = n maka x = n dengan x ≥ 1 : Hasil x dari kedua persamaan yaitu x<sup>2</sup> = 4 dan x = <math>\sqrt{4}</math> adalah berbeda. Untuk x<sup>2</sup> = 4 maka hasilnya x = <math>\pm{2}</math> sedangkan x = <math>\sqrt{4}</math> hasilnya x = 2. == Bentuk dan sifat logaritma == bentuk: <sup>a</sup>log c = b dengan {a,c} > 0 dan a ≠ 1 sifat: #log a+log b = log (axb) #log a-log b = log (a:b) #log a:log b = <sup>b</sup>log a #<sup>b</sup>log a x <sup>a</sup>log c = <sup>b</sup>log c #<sup>b</sup>log a = log a:log b #<sup>b</sup>log a = 1:<sup>a</sup>log b #<math>b^{^b log a}</math> = a #<sup>b</sup>log a<sup>m</sup> = m x <sup>b</sup>log a #<math>^{b^n}log a</math> = 1/n <sup>b</sup>log a #<math>^{b^n}log a^m</math> = m/n <sup>b</sup>log a #log a<sup>log b</sup> = log b<sup>log a</sup> = log b x log a #a<sup>log b</sup> = b<sup>log a</sup> #<sup>a</sup>log 1 = 0 #<sup>a</sup>log a = 1 contoh soal Berapa nilai x dari # x<sup>2x<sup>6</sup></sup> = 36 # x<sup>x<sup>2</sup></sup> = 16 # 6<sup>x</sup> + x = 219 # 2<sup>x</sup> + 2x = 8 # 3<sup>x</sup> + 5x = 101 ;jawaban # x<sup>2x<sup>6</sup></sup> = 36 * x<sup>2x<sup>6</sup></sup> = 6<sup>2</sup> * (x<sup>2x<sup>6</sup></sup>)<sup>3</sup> = (6<sup>2</sup>)<sup>3</sup> * (x<sup>6</sup>)<sup>x<sup>6</sup></sup> = 6<sup>6</sup> * x<sup>6</sup> = 6 * <math>x = \sqrt[6]{6}</math> # x<sup>x<sup>2</sup></sup> = 16 * x<sup>x<sup>2</sup></sup> = 4<sup>2</sup> * (x<sup>x<sup>2</sup></sup>)<sup>2</sup> = (4<sup>2</sup>)<sup>2</sup> * (x<sup>2</sup>)<sup>x<sup>2</sup></sup> = 4<sup>4</sup> * x<sup>2</sup> = 4 * <math>x = \sqrt{4}</math> * <math>x = 2</math> # ; cara biasa * 6<sup>x</sup> + x = 219 * 6<sup>x</sup> = 219 - x * 6<sup>219</sup> x 6<sup>x</sup> = (219 - x) 6<sup>219</sup> * 6<sup>219</sup> = (219 - x) 6<sup>(219 - x)</sup> * 6<sup>3</sup> x 6<sup>216</sup> = (219 - x) 6<sup>(219 - x)</sup> * 216 x 6<sup>216</sup> = (219 - x) 6<sup>(219 - x)</sup> * 216 = 219 - x * x = 3 ; fungsi lambert (W(a x e<sup>a</sup>) = a; e = bilangan euler) * 6<sup>x</sup> + x = 219 * 6<sup>x</sup> = 219 - x * 1 = (219 - x) x 6<sup>-x</sup> * 6<sup>219</sup> = (219 - x) x 6<sup>-x</sup> x 6<sup>219</sup> * 6<sup>219</sup> = (219 - x) x 6<sup>(219-x)</sup> * 6<sup>219</sup> = (219 - x) x e<sup>ln 6(219-x)</sup> * 6<sup>219</sup> = (219 - x) x e<sup>(219-x)ln 6</sup> * 6<sup>219</sup> x ln 6 = (219 - x) x ln 6 x e<sup>(219-x)ln 6</sup> * W(6<sup>219</sup> x ln 6) = W((219 - x) x ln 6 x e<sup>(219-x)ln 6</sup>) * W(6<sup>219</sup> x ln 6) = (219 - x) x ln 6 * W(6<sup>3</sup> x 6<sup>216</sup> x ln 6) = (219 - x) x ln 6 * W(216 x ln 6 x 6<sup>216</sup>) = (219 - x) x ln 6 * W(216 x ln 6 x e<sup>(ln 6 x 216)</sup>) = (219 - x) x ln 6 * W(216 x ln 6 x e<sup>(216 x ln 6)</sup>) = (219 - x) x ln 6 * 216 x ln 6 = (219 - x) x ln 6 * 216 = 219 - x * x = 3 # ; cara biasa * 2<sup>x</sup> + 2x = 8 * 2<sup>x</sup> = 8 - 2x * 2<sup>x</sup> = 2(4 - x) * 2<sup>4</sup> x 2<sup>x</sup> = 2(4 - x) 2<sup>4</sup> * <math>\frac{2^4}{2}</math> = (4 - x) 2<sup>(4 - x)</sup> * 2<sup>3</sup> = (4 - x) 2<sup>(4 - x)</sup> * 2 x 2<sup>2</sup> = (4 - x) 2<sup>(4 - x)</sup> * 2 = 4 - x * x = 2 ; fungsi lambert * 2<sup>x</sup> + 2x = 8 * 2<sup>x</sup> = 8 - 2x * 1 = (8 - 2x) x 2<sup>-x</sup> * 2<sup>4</sup> = 2(4 - x) x 2<sup>-x</sup> x 2<sup>4</sup> * 2<sup>3</sup> = (4 - x) x 2<sup>(4-x)</sup> * 2<sup>3</sup> = (4 - x) x e<sup>ln 2(4-x)</sup> * 2<sup>3</sup> = (4 - x) x e<sup>(4-x)ln 2</sup> * 2<sup>3</sup> x ln 2 = (4 - x) x ln 2 x e<sup>(4-x)ln 2</sup> * W(2<sup>3</sup> x ln 2) = W((4 - x) x ln 2 x e<sup>(4-x)ln 2</sup>) * W(2<sup>3</sup> x ln 2) = (4 - x) x ln 2 * W(2 x 2<sup>2</sup> x ln 2) = (4 - x) x ln 2 * W(2 x ln 2 x 2<sup>2</sup>) = (4 - x) x ln 2 * W(2 x ln 2 x e<sup>(ln 2 x 2)</sup>) = (4 - x) x ln 2 * W(2 x ln 2 x e<sup>(2 x ln 2)</sup>) = (4 - x) x ln 2 * 2 x ln 2 = (4 - x) x ln 2 * 2 = 4 - x * x = 2 # ; cara biasa * 3<sup>x</sup> + 5x = 101 * 3<sup>x</sup> = 101 - 5x * 3<sup>x</sup> = 5(<math>\frac{101}{5}</math> - x) * 3<sup><math>\frac{101}{5}</math></sup> x 3<sup>x</sup> = 5(<math>\frac{101}{5}</math> - x) 3<sup><math>\frac{101}{5}</math></sup> * <math>\frac{3^{\frac{101}{5}}}{5}</math> = (<math>\frac{101}{5}</math> - x) 3<sup>(<math>\frac{101}{5}</math> - x)</sup> * <math>\frac{1}{5}</math> 3<sup><math>\frac{20}{5}</math></sup> 3<sup><math>\frac{81}{5}</math></sup> = (<math>\frac{101}{5}</math> - x) 3<sup>(<math>\frac{101}{5}</math> - x)</sup> * <math>\frac{1}{5}</math> 3<sup>4</sup> 3<sup><math>\frac{81}{5}</math></sup> = (<math>\frac{101}{5}</math> - x) 3<sup>(<math>\frac{101}{5}</math> - x)</sup> * <math>\frac{81}{5}</math> x 3<sup><math>\frac{81}{5}</math></sup> = (<math>\frac{101}{5}</math> - x) 3<sup>(<math>\frac{101}{5}</math> - x)</sup> * <math>\frac{81}{5}</math> = <math>\frac{101}{5}</math> - x * x = <math>\frac{101}{5} - \frac{81}{5}</math> * x = <math>\frac{20}{5}</math> * x = 4 ; fungsi lambert * 3<sup>x</sup> + 5x = 101 * 3<sup>x</sup> = 101 - 5x * 1 = (101 - 5x) x 3<sup>-x</sup> * 3<sup><math>\frac{101}{5}</math></sup> = 5(<math>\frac{101}{5}</math> - x) x 3<sup>-x</sup> x 3<sup><math>\frac{101}{5}</math></sup> * <math>\frac{3^{\frac{101}{5}}}{5}</math> = (<math>\frac{101}{5}</math> - x) x 3<sup>(<math>\frac{101}{5}</math>-x)</sup> * <math>\frac{3^{\frac{101}{5}}}{5}</math> = (<math>\frac{101}{5}</math> - x) x e<sup>ln 3(<math>\frac{101}{5}</math>-x)</sup> * <math>\frac{3^{\frac{101}{5}}}{5}</math> = (<math>\frac{101}{5}</math> - x) x e<sup>(<math>\frac{101}{5}</math>-x)ln 3</sup> * <math>\frac{3^{\frac{101}{5}}}{5}</math> x ln 3 = (<math>\frac{101}{5}</math> - x) x ln 3 x e<sup>(<math>\frac{101}{5}</math>-x)ln 3</sup> * W(<math>\frac{3^{\frac{101}{5}}}{5}</math> x ln 3) = W((<math>\frac{101}{5}</math> - x) x ln 3 x e<sup>(<math>\frac{101}{5}</math>-x)ln 3</sup>) * W(<math>\frac{3^{\frac{101}{5}}}{5}</math> x ln 3) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{3^{\frac{20}{5}} \cdot 3^{\frac{81}{5}}}{5}</math> x ln 3) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{3^{\frac{20}{5}}}{5}</math> x ln 3 x <math>3^{\frac{81}{5}}</math>) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{3^{4}}{5}</math> x ln 3 x <math>3^{\frac{81}{5}}</math>) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{81}{5}</math> x ln 3 x <math>3^{\frac{81}{5}}</math>) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{81}{5}</math> x ln 3 x e<sup>(ln 3 x <math>\frac{81}{5}</math>)</sup>) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{81}{5}</math> x ln 3 x e<sup>(<math>\frac{81}{5}</math> x ln 3)</sup>) = (<math>\frac{101}{5}</math> - x) x ln 3 * <math>\frac{81}{5}</math> x ln 3 = (<math>\frac{101}{5}</math> - x) x ln 3 * <math>\frac{81}{5}</math> = <math>\frac{101}{5}</math> - x * x = <math>\frac{101}{5}</math> - <math>\frac{81}{5}</math> * x = <math>\frac{20}{5}</math> * x = 4 ; contoh soal # Tentukan nilai dari <math>\sqrt[3]{5+2\sqrt{3}}+\sqrt[3]{5-2\sqrt{3}}</math>! <div class="toccolours mw-collapsible mw-collapsed" style="width:550px"><div style="font-weight:bold;line-height:1.6;">Jawaban</div> <div class="mw-collapsible-content"> <math display="block"> \begin{align} \sqrt[3]{5+2\sqrt{3}}+\sqrt[3]{5-2\sqrt{3}} \end{align} </math> </div></div> [[Kategori:Soal-Soal Matematika]] jl8wk6al2qmjt8twtlpken0mo5nq95m 108330 108328 2025-07-07T10:17:43Z Akuindo 8654 108330 wikitext text/x-wiki == Bentuk dan sifat eksponen == bentuk: a<sup>b</sup> = c sifat: #a<sup>m</sup>xa<sup>n</sup> = a<sup>m+n</sup> #a<sup>m</sup>:a<sup>n</sup> = a<sup>m-n</sup> #(a<sup>m</sup>)<sup>n</sup> = a<sup>mxn</sup> #<math>\sqrt[n]{a^m}</math> = a<sup>m/n</sup> #a<sup>m</sup>xb<sup>m</sup> = (axb)<sup>m</sup> #a<sup>m</sup>:b<sup>m</sup> = (a:b)<sup>m</sup> #a<sup>-m</sup> = <math>\frac{1}{a^m}</math> #a<sup>m<sup>n</sup></sup> = a<sup>(m<sup>n</sup>)</sup> #(a<sup>m</sup>)<sup>n</sup> ≠ a<sup>m<sup>n</sup></sup> #0<sup>a</sup> = 0 dengan a > 0 #a<sup>0</sup> = 1 dengan a ≠ 0 #0:a = 0 dengan a ≠ 0 #a<sup>1</sup> = a #a<sup>-1</sup> = <math>\frac{1}{a}</math> dengan a ≠ 0 #a<sup>a</sup> = b<sup>b</sup> dimana a = b ; Tambahan : x<sup>x<sup>……</sup><sup>n</sup></sup> = n maka <math>x = \sqrt[n]{n}</math> dengan x ≥ 1 : x<sup>x<sup>n</sup></sup> = n maka x = n dengan x ≥ 1 : Hasil x dari kedua persamaan yaitu x<sup>2</sup> = 4 dan x = <math>\sqrt{4}</math> adalah berbeda. Untuk x<sup>2</sup> = 4 maka hasilnya x = <math>\pm{2}</math> sedangkan x = <math>\sqrt{4}</math> hasilnya x = 2. == Bentuk dan sifat logaritma == bentuk: <sup>a</sup>log c = b dengan {a,c} > 0 dan a ≠ 1 sifat: #log a+log b = log (axb) #log a-log b = log (a:b) #log a:log b = <sup>b</sup>log a #<sup>b</sup>log a x <sup>a</sup>log c = <sup>b</sup>log c #<sup>b</sup>log a = log a:log b #<sup>b</sup>log a = 1:<sup>a</sup>log b #<math>b^{^b log a}</math> = a #<sup>b</sup>log a<sup>m</sup> = m x <sup>b</sup>log a #<math>^{b^n}log a</math> = 1/n <sup>b</sup>log a #<math>^{b^n}log a^m</math> = m/n <sup>b</sup>log a #log a<sup>log b</sup> = log b<sup>log a</sup> = log b x log a #a<sup>log b</sup> = b<sup>log a</sup> #<sup>a</sup>log 1 = 0 #<sup>a</sup>log a = 1 contoh soal Berapa nilai x dari # x<sup>2x<sup>6</sup></sup> = 36 # x<sup>x<sup>2</sup></sup> = 16 # 6<sup>x</sup> + x = 219 # 2<sup>x</sup> + 2x = 8 # 3<sup>x</sup> + 5x = 101 ;jawaban # x<sup>2x<sup>6</sup></sup> = 36 * x<sup>2x<sup>6</sup></sup> = 6<sup>2</sup> * (x<sup>2x<sup>6</sup></sup>)<sup>3</sup> = (6<sup>2</sup>)<sup>3</sup> * (x<sup>6</sup>)<sup>x<sup>6</sup></sup> = 6<sup>6</sup> * x<sup>6</sup> = 6 * <math>x = \sqrt[6]{6}</math> # x<sup>x<sup>2</sup></sup> = 16 * x<sup>x<sup>2</sup></sup> = 4<sup>2</sup> * (x<sup>x<sup>2</sup></sup>)<sup>2</sup> = (4<sup>2</sup>)<sup>2</sup> * (x<sup>2</sup>)<sup>x<sup>2</sup></sup> = 4<sup>4</sup> * x<sup>2</sup> = 4 * <math>x = \sqrt{4}</math> * <math>x = 2</math> # ; cara biasa * 6<sup>x</sup> + x = 219 * 6<sup>x</sup> = 219 - x * 6<sup>219</sup> x 6<sup>x</sup> = (219 - x) 6<sup>219</sup> * 6<sup>219</sup> = (219 - x) 6<sup>(219 - x)</sup> * 6<sup>3</sup> x 6<sup>216</sup> = (219 - x) 6<sup>(219 - x)</sup> * 216 x 6<sup>216</sup> = (219 - x) 6<sup>(219 - x)</sup> * 216 = 219 - x * x = 3 ; fungsi lambert (W(a x e<sup>a</sup>) = a; e = bilangan euler) * 6<sup>x</sup> + x = 219 * 6<sup>x</sup> = 219 - x * 1 = (219 - x) x 6<sup>-x</sup> * 6<sup>219</sup> = (219 - x) x 6<sup>-x</sup> x 6<sup>219</sup> * 6<sup>219</sup> = (219 - x) x 6<sup>(219-x)</sup> * 6<sup>219</sup> = (219 - x) x e<sup>ln 6(219-x)</sup> * 6<sup>219</sup> = (219 - x) x e<sup>(219-x)ln 6</sup> * 6<sup>219</sup> x ln 6 = (219 - x) x ln 6 x e<sup>(219-x)ln 6</sup> * W(6<sup>219</sup> x ln 6) = W((219 - x) x ln 6 x e<sup>(219-x)ln 6</sup>) * W(6<sup>219</sup> x ln 6) = (219 - x) x ln 6 * W(6<sup>3</sup> x 6<sup>216</sup> x ln 6) = (219 - x) x ln 6 * W(216 x ln 6 x 6<sup>216</sup>) = (219 - x) x ln 6 * W(216 x ln 6 x e<sup>(ln 6 x 216)</sup>) = (219 - x) x ln 6 * W(216 x ln 6 x e<sup>(216 x ln 6)</sup>) = (219 - x) x ln 6 * 216 x ln 6 = (219 - x) x ln 6 * 216 = 219 - x * x = 3 # ; cara biasa * 2<sup>x</sup> + 2x = 8 * 2<sup>x</sup> = 8 - 2x * 2<sup>x</sup> = 2(4 - x) * 2<sup>4</sup> x 2<sup>x</sup> = 2(4 - x) 2<sup>4</sup> * <math>\frac{2^4}{2}</math> = (4 - x) 2<sup>(4 - x)</sup> * 2<sup>3</sup> = (4 - x) 2<sup>(4 - x)</sup> * 2 x 2<sup>2</sup> = (4 - x) 2<sup>(4 - x)</sup> * 2 = 4 - x * x = 2 ; fungsi lambert * 2<sup>x</sup> + 2x = 8 * 2<sup>x</sup> = 8 - 2x * 1 = (8 - 2x) x 2<sup>-x</sup> * 2<sup>4</sup> = 2(4 - x) x 2<sup>-x</sup> x 2<sup>4</sup> * 2<sup>3</sup> = (4 - x) x 2<sup>(4-x)</sup> * 2<sup>3</sup> = (4 - x) x e<sup>ln 2(4-x)</sup> * 2<sup>3</sup> = (4 - x) x e<sup>(4-x)ln 2</sup> * 2<sup>3</sup> x ln 2 = (4 - x) x ln 2 x e<sup>(4-x)ln 2</sup> * W(2<sup>3</sup> x ln 2) = W((4 - x) x ln 2 x e<sup>(4-x)ln 2</sup>) * W(2<sup>3</sup> x ln 2) = (4 - x) x ln 2 * W(2 x 2<sup>2</sup> x ln 2) = (4 - x) x ln 2 * W(2 x ln 2 x 2<sup>2</sup>) = (4 - x) x ln 2 * W(2 x ln 2 x e<sup>(ln 2 x 2)</sup>) = (4 - x) x ln 2 * W(2 x ln 2 x e<sup>(2 x ln 2)</sup>) = (4 - x) x ln 2 * 2 x ln 2 = (4 - x) x ln 2 * 2 = 4 - x * x = 2 # ; cara biasa * 3<sup>x</sup> + 5x = 101 * 3<sup>x</sup> = 101 - 5x * 3<sup>x</sup> = 5(<math>\frac{101}{5}</math> - x) * 3<sup><math>\frac{101}{5}</math></sup> x 3<sup>x</sup> = 5(<math>\frac{101}{5}</math> - x) 3<sup><math>\frac{101}{5}</math></sup> * <math>\frac{3^{\frac{101}{5}}}{5}</math> = (<math>\frac{101}{5}</math> - x) 3<sup>(<math>\frac{101}{5}</math> - x)</sup> * <math>\frac{1}{5}</math> 3<sup><math>\frac{20}{5}</math></sup> 3<sup><math>\frac{81}{5}</math></sup> = (<math>\frac{101}{5}</math> - x) 3<sup>(<math>\frac{101}{5}</math> - x)</sup> * <math>\frac{1}{5}</math> 3<sup>4</sup> 3<sup><math>\frac{81}{5}</math></sup> = (<math>\frac{101}{5}</math> - x) 3<sup>(<math>\frac{101}{5}</math> - x)</sup> * <math>\frac{81}{5}</math> x 3<sup><math>\frac{81}{5}</math></sup> = (<math>\frac{101}{5}</math> - x) 3<sup>(<math>\frac{101}{5}</math> - x)</sup> * <math>\frac{81}{5}</math> = <math>\frac{101}{5}</math> - x * x = <math>\frac{101}{5} - \frac{81}{5}</math> * x = <math>\frac{20}{5}</math> * x = 4 ; fungsi lambert * 3<sup>x</sup> + 5x = 101 * 3<sup>x</sup> = 101 - 5x * 1 = (101 - 5x) x 3<sup>-x</sup> * 3<sup><math>\frac{101}{5}</math></sup> = 5(<math>\frac{101}{5}</math> - x) x 3<sup>-x</sup> x 3<sup><math>\frac{101}{5}</math></sup> * <math>\frac{3^{\frac{101}{5}}}{5}</math> = (<math>\frac{101}{5}</math> - x) x 3<sup>(<math>\frac{101}{5}</math>-x)</sup> * <math>\frac{3^{\frac{101}{5}}}{5}</math> = (<math>\frac{101}{5}</math> - x) x e<sup>ln 3(<math>\frac{101}{5}</math>-x)</sup> * <math>\frac{3^{\frac{101}{5}}}{5}</math> = (<math>\frac{101}{5}</math> - x) x e<sup>(<math>\frac{101}{5}</math>-x)ln 3</sup> * <math>\frac{3^{\frac{101}{5}}}{5}</math> x ln 3 = (<math>\frac{101}{5}</math> - x) x ln 3 x e<sup>(<math>\frac{101}{5}</math>-x)ln 3</sup> * W(<math>\frac{3^{\frac{101}{5}}}{5}</math> x ln 3) = W((<math>\frac{101}{5}</math> - x) x ln 3 x e<sup>(<math>\frac{101}{5}</math>-x)ln 3</sup>) * W(<math>\frac{3^{\frac{101}{5}}}{5}</math> x ln 3) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{3^{\frac{20}{5}} \cdot 3^{\frac{81}{5}}}{5}</math> x ln 3) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{3^{\frac{20}{5}}}{5}</math> x ln 3 x <math>3^{\frac{81}{5}}</math>) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{3^{4}}{5}</math> x ln 3 x <math>3^{\frac{81}{5}}</math>) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{81}{5}</math> x ln 3 x <math>3^{\frac{81}{5}}</math>) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{81}{5}</math> x ln 3 x e<sup>(ln 3 x <math>\frac{81}{5}</math>)</sup>) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{81}{5}</math> x ln 3 x e<sup>(<math>\frac{81}{5}</math> x ln 3)</sup>) = (<math>\frac{101}{5}</math> - x) x ln 3 * <math>\frac{81}{5}</math> x ln 3 = (<math>\frac{101}{5}</math> - x) x ln 3 * <math>\frac{81}{5}</math> = <math>\frac{101}{5}</math> - x * x = <math>\frac{101}{5}</math> - <math>\frac{81}{5}</math> * x = <math>\frac{20}{5}</math> * x = 4 ; contoh soal # Tentukan nilai dari <math>\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}</math>! <div class="toccolours mw-collapsible mw-collapsed" style="width:550px"><div style="font-weight:bold;line-height:1.6;">Jawaban</div> <div class="mw-collapsible-content"> <math display="block"> \begin{align} \sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}} \\ \text{misal } \sqrt[3]{5+2\sqrt{13}}=a \text{ dan } \sqrt[3]{5-2\sqrt{13}}=b \text{ maka menjadi } a+b=p \\ a+b &= p \\ (a+b)^3 &= p^3 \\ a^3+b^3+3ab(a+b) &= p^3 \\ a^3+b^3 &= (\sqrt[3]{5+2\sqrt{13}})^3+(\sqrt[3]{5-2\sqrt{13}})^3 \\ &= 5+2\sqrt{13}+5-2\sqrt{13} \\ &= 10 \\ ab &= (\sqrt[3]{5+2\sqrt{13}})\cdot(\sqrt[3]{5-2\sqrt{13}}) \\ &= \sqrt[3]{(5+2\sqrt{13})(5-2\sqrt{13}} \\ &= \sqrt[3]{25-52} \\ &= \sqrt[3]{-27} \\ &= -3 \\ a^3+b^3+3ab(a+b) &= p^3 \\ 10+3(-3)p &= p^3 \\ 10-9p &= p^3 \\ p^3+9p-10 &= 0 \\ (p-1)(p^2+p+10) &= 0 \\ p=1 &\text{ atau (definit positif) } \\ \end{align} </math> </div></div> [[Kategori:Soal-Soal Matematika]] 7ziltd4f23jasz9jh5jgf22hzr2oz1n 108331 108330 2025-07-07T10:19:12Z Akuindo 8654 108331 wikitext text/x-wiki == Bentuk dan sifat eksponen == bentuk: a<sup>b</sup> = c sifat: #a<sup>m</sup>xa<sup>n</sup> = a<sup>m+n</sup> #a<sup>m</sup>:a<sup>n</sup> = a<sup>m-n</sup> #(a<sup>m</sup>)<sup>n</sup> = a<sup>mxn</sup> #<math>\sqrt[n]{a^m}</math> = a<sup>m/n</sup> #a<sup>m</sup>xb<sup>m</sup> = (axb)<sup>m</sup> #a<sup>m</sup>:b<sup>m</sup> = (a:b)<sup>m</sup> #a<sup>-m</sup> = <math>\frac{1}{a^m}</math> #a<sup>m<sup>n</sup></sup> = a<sup>(m<sup>n</sup>)</sup> #(a<sup>m</sup>)<sup>n</sup> ≠ a<sup>m<sup>n</sup></sup> #0<sup>a</sup> = 0 dengan a > 0 #a<sup>0</sup> = 1 dengan a ≠ 0 #0:a = 0 dengan a ≠ 0 #a<sup>1</sup> = a #a<sup>-1</sup> = <math>\frac{1}{a}</math> dengan a ≠ 0 #a<sup>a</sup> = b<sup>b</sup> dimana a = b ; Tambahan : x<sup>x<sup>……</sup><sup>n</sup></sup> = n maka <math>x = \sqrt[n]{n}</math> dengan x ≥ 1 : x<sup>x<sup>n</sup></sup> = n maka x = n dengan x ≥ 1 : Hasil x dari kedua persamaan yaitu x<sup>2</sup> = 4 dan x = <math>\sqrt{4}</math> adalah berbeda. Untuk x<sup>2</sup> = 4 maka hasilnya x = <math>\pm{2}</math> sedangkan x = <math>\sqrt{4}</math> hasilnya x = 2. == Bentuk dan sifat logaritma == bentuk: <sup>a</sup>log c = b dengan {a,c} > 0 dan a ≠ 1 sifat: #log a+log b = log (axb) #log a-log b = log (a:b) #log a:log b = <sup>b</sup>log a #<sup>b</sup>log a x <sup>a</sup>log c = <sup>b</sup>log c #<sup>b</sup>log a = log a:log b #<sup>b</sup>log a = 1:<sup>a</sup>log b #<math>b^{^b log a}</math> = a #<sup>b</sup>log a<sup>m</sup> = m x <sup>b</sup>log a #<math>^{b^n}log a</math> = 1/n <sup>b</sup>log a #<math>^{b^n}log a^m</math> = m/n <sup>b</sup>log a #log a<sup>log b</sup> = log b<sup>log a</sup> = log b x log a #a<sup>log b</sup> = b<sup>log a</sup> #<sup>a</sup>log 1 = 0 #<sup>a</sup>log a = 1 contoh soal Berapa nilai x dari # x<sup>2x<sup>6</sup></sup> = 36 # x<sup>x<sup>2</sup></sup> = 16 # 6<sup>x</sup> + x = 219 # 2<sup>x</sup> + 2x = 8 # 3<sup>x</sup> + 5x = 101 ;jawaban # x<sup>2x<sup>6</sup></sup> = 36 * x<sup>2x<sup>6</sup></sup> = 6<sup>2</sup> * (x<sup>2x<sup>6</sup></sup>)<sup>3</sup> = (6<sup>2</sup>)<sup>3</sup> * (x<sup>6</sup>)<sup>x<sup>6</sup></sup> = 6<sup>6</sup> * x<sup>6</sup> = 6 * <math>x = \sqrt[6]{6}</math> # x<sup>x<sup>2</sup></sup> = 16 * x<sup>x<sup>2</sup></sup> = 4<sup>2</sup> * (x<sup>x<sup>2</sup></sup>)<sup>2</sup> = (4<sup>2</sup>)<sup>2</sup> * (x<sup>2</sup>)<sup>x<sup>2</sup></sup> = 4<sup>4</sup> * x<sup>2</sup> = 4 * <math>x = \sqrt{4}</math> * <math>x = 2</math> # ; cara biasa * 6<sup>x</sup> + x = 219 * 6<sup>x</sup> = 219 - x * 6<sup>219</sup> x 6<sup>x</sup> = (219 - x) 6<sup>219</sup> * 6<sup>219</sup> = (219 - x) 6<sup>(219 - x)</sup> * 6<sup>3</sup> x 6<sup>216</sup> = (219 - x) 6<sup>(219 - x)</sup> * 216 x 6<sup>216</sup> = (219 - x) 6<sup>(219 - x)</sup> * 216 = 219 - x * x = 3 ; fungsi lambert (W(a x e<sup>a</sup>) = a; e = bilangan euler) * 6<sup>x</sup> + x = 219 * 6<sup>x</sup> = 219 - x * 1 = (219 - x) x 6<sup>-x</sup> * 6<sup>219</sup> = (219 - x) x 6<sup>-x</sup> x 6<sup>219</sup> * 6<sup>219</sup> = (219 - x) x 6<sup>(219-x)</sup> * 6<sup>219</sup> = (219 - x) x e<sup>ln 6(219-x)</sup> * 6<sup>219</sup> = (219 - x) x e<sup>(219-x)ln 6</sup> * 6<sup>219</sup> x ln 6 = (219 - x) x ln 6 x e<sup>(219-x)ln 6</sup> * W(6<sup>219</sup> x ln 6) = W((219 - x) x ln 6 x e<sup>(219-x)ln 6</sup>) * W(6<sup>219</sup> x ln 6) = (219 - x) x ln 6 * W(6<sup>3</sup> x 6<sup>216</sup> x ln 6) = (219 - x) x ln 6 * W(216 x ln 6 x 6<sup>216</sup>) = (219 - x) x ln 6 * W(216 x ln 6 x e<sup>(ln 6 x 216)</sup>) = (219 - x) x ln 6 * W(216 x ln 6 x e<sup>(216 x ln 6)</sup>) = (219 - x) x ln 6 * 216 x ln 6 = (219 - x) x ln 6 * 216 = 219 - x * x = 3 # ; cara biasa * 2<sup>x</sup> + 2x = 8 * 2<sup>x</sup> = 8 - 2x * 2<sup>x</sup> = 2(4 - x) * 2<sup>4</sup> x 2<sup>x</sup> = 2(4 - x) 2<sup>4</sup> * <math>\frac{2^4}{2}</math> = (4 - x) 2<sup>(4 - x)</sup> * 2<sup>3</sup> = (4 - x) 2<sup>(4 - x)</sup> * 2 x 2<sup>2</sup> = (4 - x) 2<sup>(4 - x)</sup> * 2 = 4 - x * x = 2 ; fungsi lambert * 2<sup>x</sup> + 2x = 8 * 2<sup>x</sup> = 8 - 2x * 1 = (8 - 2x) x 2<sup>-x</sup> * 2<sup>4</sup> = 2(4 - x) x 2<sup>-x</sup> x 2<sup>4</sup> * 2<sup>3</sup> = (4 - x) x 2<sup>(4-x)</sup> * 2<sup>3</sup> = (4 - x) x e<sup>ln 2(4-x)</sup> * 2<sup>3</sup> = (4 - x) x e<sup>(4-x)ln 2</sup> * 2<sup>3</sup> x ln 2 = (4 - x) x ln 2 x e<sup>(4-x)ln 2</sup> * W(2<sup>3</sup> x ln 2) = W((4 - x) x ln 2 x e<sup>(4-x)ln 2</sup>) * W(2<sup>3</sup> x ln 2) = (4 - x) x ln 2 * W(2 x 2<sup>2</sup> x ln 2) = (4 - x) x ln 2 * W(2 x ln 2 x 2<sup>2</sup>) = (4 - x) x ln 2 * W(2 x ln 2 x e<sup>(ln 2 x 2)</sup>) = (4 - x) x ln 2 * W(2 x ln 2 x e<sup>(2 x ln 2)</sup>) = (4 - x) x ln 2 * 2 x ln 2 = (4 - x) x ln 2 * 2 = 4 - x * x = 2 # ; cara biasa * 3<sup>x</sup> + 5x = 101 * 3<sup>x</sup> = 101 - 5x * 3<sup>x</sup> = 5(<math>\frac{101}{5}</math> - x) * 3<sup><math>\frac{101}{5}</math></sup> x 3<sup>x</sup> = 5(<math>\frac{101}{5}</math> - x) 3<sup><math>\frac{101}{5}</math></sup> * <math>\frac{3^{\frac{101}{5}}}{5}</math> = (<math>\frac{101}{5}</math> - x) 3<sup>(<math>\frac{101}{5}</math> - x)</sup> * <math>\frac{1}{5}</math> 3<sup><math>\frac{20}{5}</math></sup> 3<sup><math>\frac{81}{5}</math></sup> = (<math>\frac{101}{5}</math> - x) 3<sup>(<math>\frac{101}{5}</math> - x)</sup> * <math>\frac{1}{5}</math> 3<sup>4</sup> 3<sup><math>\frac{81}{5}</math></sup> = (<math>\frac{101}{5}</math> - x) 3<sup>(<math>\frac{101}{5}</math> - x)</sup> * <math>\frac{81}{5}</math> x 3<sup><math>\frac{81}{5}</math></sup> = (<math>\frac{101}{5}</math> - x) 3<sup>(<math>\frac{101}{5}</math> - x)</sup> * <math>\frac{81}{5}</math> = <math>\frac{101}{5}</math> - x * x = <math>\frac{101}{5} - \frac{81}{5}</math> * x = <math>\frac{20}{5}</math> * x = 4 ; fungsi lambert * 3<sup>x</sup> + 5x = 101 * 3<sup>x</sup> = 101 - 5x * 1 = (101 - 5x) x 3<sup>-x</sup> * 3<sup><math>\frac{101}{5}</math></sup> = 5(<math>\frac{101}{5}</math> - x) x 3<sup>-x</sup> x 3<sup><math>\frac{101}{5}</math></sup> * <math>\frac{3^{\frac{101}{5}}}{5}</math> = (<math>\frac{101}{5}</math> - x) x 3<sup>(<math>\frac{101}{5}</math>-x)</sup> * <math>\frac{3^{\frac{101}{5}}}{5}</math> = (<math>\frac{101}{5}</math> - x) x e<sup>ln 3(<math>\frac{101}{5}</math>-x)</sup> * <math>\frac{3^{\frac{101}{5}}}{5}</math> = (<math>\frac{101}{5}</math> - x) x e<sup>(<math>\frac{101}{5}</math>-x)ln 3</sup> * <math>\frac{3^{\frac{101}{5}}}{5}</math> x ln 3 = (<math>\frac{101}{5}</math> - x) x ln 3 x e<sup>(<math>\frac{101}{5}</math>-x)ln 3</sup> * W(<math>\frac{3^{\frac{101}{5}}}{5}</math> x ln 3) = W((<math>\frac{101}{5}</math> - x) x ln 3 x e<sup>(<math>\frac{101}{5}</math>-x)ln 3</sup>) * W(<math>\frac{3^{\frac{101}{5}}}{5}</math> x ln 3) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{3^{\frac{20}{5}} \cdot 3^{\frac{81}{5}}}{5}</math> x ln 3) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{3^{\frac{20}{5}}}{5}</math> x ln 3 x <math>3^{\frac{81}{5}}</math>) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{3^{4}}{5}</math> x ln 3 x <math>3^{\frac{81}{5}}</math>) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{81}{5}</math> x ln 3 x <math>3^{\frac{81}{5}}</math>) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{81}{5}</math> x ln 3 x e<sup>(ln 3 x <math>\frac{81}{5}</math>)</sup>) = (<math>\frac{101}{5}</math> - x) x ln 3 * W(<math>\frac{81}{5}</math> x ln 3 x e<sup>(<math>\frac{81}{5}</math> x ln 3)</sup>) = (<math>\frac{101}{5}</math> - x) x ln 3 * <math>\frac{81}{5}</math> x ln 3 = (<math>\frac{101}{5}</math> - x) x ln 3 * <math>\frac{81}{5}</math> = <math>\frac{101}{5}</math> - x * x = <math>\frac{101}{5}</math> - <math>\frac{81}{5}</math> * x = <math>\frac{20}{5}</math> * x = 4 ; contoh soal # Tentukan nilai dari <math>\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}</math>! <div class="toccolours mw-collapsible mw-collapsed" style="width:550px"><div style="font-weight:bold;line-height:1.6;">Jawaban</div> <div class="mw-collapsible-content"> <math display="block"> \begin{align} \sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}} \\ \text{misal } \sqrt[3]{5+2\sqrt{13}}=a \text{ dan } \sqrt[3]{5-2\sqrt{13}}=b \text{ maka menjadi } a+b=p \\ a+b &= p \\ (a+b)^3 &= p^3 \\ a^3+b^3+3ab(a+b) &= p^3 \\ a^3+b^3 &= (\sqrt[3]{5+2\sqrt{13}})^3+(\sqrt[3]{5-2\sqrt{13}})^3 \\ &= 5+2\sqrt{13}+5-2\sqrt{13} \\ &= 10 \\ ab &= (\sqrt[3]{5+2\sqrt{13}})\cdot(\sqrt[3]{5-2\sqrt{13}}) \\ &= \sqrt[3]{(5+2\sqrt{13})(5-2\sqrt{13})} \\ &= \sqrt[3]{25-52} \\ &= \sqrt[3]{-27} \\ &= -3 \\ a^3+b^3+3ab(a+b) &= p^3 \\ 10+3(-3)p &= p^3 \\ 10-9p &= p^3 \\ p^3+9p-10 &= 0 \\ (p-1)(p^2+p+10) &= 0 \\ p=1 &\text{ atau (definit positif) } \\ \end{align} </math> </div></div> [[Kategori:Soal-Soal Matematika]] ne99m632hxu6opw4o20mwc9trfw1g88 Soal-Soal Matematika/Bangun datar 0 23127 108313 108312 2025-07-06T12:05:20Z Akuindo 8654 108313 wikitext text/x-wiki Bangun datar disebut juga dimensi dua yang memiliki sebidang serta beberapa rusuknya. bangun ini memiliki simetri lipat, simetri putar dan sumbu simetri {| class="wikitable" |+ |- ! bangun datar !! simetri lipat !! simetri putar !! sumbu simetri |- | persegi || 4 || 4 || 4 |- | segi-n || || || |- | persegi panjang || 2 || 2 || 2 |- | segitiga sama sisi || 3 || 3 || 3 |- | segitiga sama kaki || 1 || 0 || 1 |- | segitiga siku-siku || 1 || 0 || 1 |- | lingkaran || takhingga || takhingga || takhingga |- | jajar genjang || 0 || 2 || 0 |- | belah ketupat || 2 || 2 || 2 |- | trapesium sama kaki || 1 || 0 || 1 |- | trapesium siku-siku || 0 || 0 || 0 |- | layang-layang || 1 || 0 || 1 |- | elips || 2 || 0 || 2 |} ; Besar sudut keliling dan sudut pusat : sudut pusat = 2 x sudut keliling ; Hubungan ketiga sisi segitiga dengan jari-jari lingkaran (lingkaran dalam segitiga siku-siku): <math>r = \frac{a+b-c}{2}</math> <div class="toccolours mw-collapsible mw-collapsed" style="width:550px"><div style="font-weight:bold;line-height:1.6;">Pembuktian</div> <div class="mw-collapsible-content"> <math display="block"> \begin{align} a-r + b-r &= c \\ a+b-2r &= c \\ 2r &= a+b-c \\ r &= \frac{a+b-c}{2} \\ \end{align} </math> </div></div> ; Hubungan dua tali busur dengan jari-jari lingkaran: <math>r = \sqrt{\frac{a^2 + b^2 + c^2 + d^2}{4}}</math> <div class="toccolours mw-collapsible mw-collapsed" style="width:550px"><div style="font-weight:bold;line-height:1.6;">Pembuktian</div> <div class="mw-collapsible-content"> <math display="block"> \begin{align} \text{ misalkan } p &= \frac{c+d}{2} \text{ dan } q = \frac{a+b}{2} \\ \text{ misalkan persegi panjang dibuat x dan y} & \\ x + p &= d \\ x + \frac{c+d}{2} &= d \\ x &= d - \frac{c+d}{2} \\ x &= \frac{d-c}{2} \\ y + q &= b \\ y + \frac{a+b}{2} &= b \\ y &= b - \frac{a+b}{2} \\ y &= \frac{b-a}{2} \\ y^2 + p^2 &= r^2 \\ (\frac{b-a}{2})^2 + (\frac{c+d}{2})^2 &= r^2 \\ \frac{a^2-2ab+b^2}{4} + \frac{c^2+2cd+d^2}{4} &= r^2 \\ x^2 + q^2 &= r^2 \\ (\frac{d-c}{2})^2 + (\frac{a+b}{2})^2 &= r^2 \\ \frac{c^2-2cd+d^2}{4} + \frac{a^2+2ab+b^2}{4} &= r^2 \\ \text {jumlah dua persamaan tersebut menjadi } & \\ \frac{a^2-2ab+b^2}{4} + \frac{c^2+2cd+d^2}{4} + \frac{c^2-2cd+d^2}{4} + \frac{a^2+2ab+b^2}{4} &= 2r^2 \\ \frac{2a^2+2b^2+2c^2+2d^2}{4} &= 2r^2 \\ \frac{2(a^2+b^2+c^2+d^2)}{4} &= 2r^2 \\ \frac{a^2+b^2+c^2+d^2}{4} &= r^2 \\ a^2+b^2+c^2+d^2 &= 4r^2 \\ r &= \sqrt{\frac{a^2 + b^2 + c^2 + d^2}{4}} \\ \end{align} </math> </div></div> ; Lingkaran dalam segitiga: <math>r = \frac{L}{s}</math> (s adalah setengah keliling segitiga) <div class="toccolours mw-collapsible mw-collapsed" style="width:550px"><div style="font-weight:bold;line-height:1.6;">Pembuktian</div> <div class="mw-collapsible-content"> <math display="block"> \begin{align} \text{ misalkan luas segitiga AOC } L_a &= \frac{ra}{2} \\ \text{ misalkan luas segitiga COB } L_b &= \frac{rb}{2} \\ \text{ misalkan luas segitiga BOC } L_c &= \frac{rc}{2} \\ \text{ maka total luas ketiga segitiga tersebut adalah } L &= L_a + L_b + L_c \\ &= \frac{ra}{2} + \frac{rb}{2} + \frac{rc}{2} \\ &= r \frac{a+b+c}{2} \\ &= r s \\ r &= \frac{L}{s} \\ \end{align} </math> </div></div> ; Lingkaran luar segitiga: <math>r = \frac{abc}{4L}</math> <div class="toccolours mw-collapsible mw-collapsed" style="width:550px"><div style="font-weight:bold;line-height:1.6;">Pembuktian</div> <div class="mw-collapsible-content"> <math display="block"> \begin{align} \text{ lihat posisi kesebangunan } \frac{t}{b} &= \frac{c}{2r} \\ t &= \frac{bc}{2r} \\ L &= \frac{at}{2} \\ &= \frac{abc}{2(2r)} \\ r &= \frac{abc}{4L} \\ \end{align} </math> </div></div> ; Garis singgung (satu) lingkaran: <math>d = \sqrt{a^2-b^2}</math> ; Garis singgung persekutuan dalam (dua) lingkaran: <math>d = \sqrt{p^2-(R+r)^2}</math> ; Garis singgung persekutuan luar (dua) lingkaran: <math>d = \sqrt{p^2-(R-r)^2}</math> keterangan: : d = panjang singgung persekutuan dalam/luar lingkaran : p = jarak kedua titik pusat lingkaran ; Teorema Ceva: AF x BD x CE = BF x CD x AE ; Teorema de Pitot: AB + DC = AD + BC (segiempat luar lingkaran) ; Teorema Power de Point: (segiempat dalam lingkaran) :: AE x EC = BE x ED ; Tali busur pada satu titik di luar lingkaran: :: AB<sup>2</sup> = AD x AE :: AB x AC = AD x AE ; Teorema Ptolomeos (segiempat dalam lingkaran) : AC x BD = AB x DC + AD x BC ; Titik E adalah pertemuan kedua perpanjangan tali busur yang bertemu. :: maka sudut E = 1/2 (sudut besar-sudut kecil) ; Hubungan besar sudut, luas juring dan panjang busur : <math>\frac{\text{besar sudut AOB }}{\text{besar sudut COD }} = \frac{\text{luas juring AOB }}{\text{luas juring COD }} = \frac{\text{panjang busur AB }}{\text{panjang busur CD }}</math> [[Kategori:Soal-Soal Matematika]] qxww8tj5liapttxmwrb94iusn8clh6x 108314 108313 2025-07-06T12:07:47Z Akuindo 8654 108314 wikitext text/x-wiki Bangun datar disebut juga dimensi dua yang memiliki sebidang serta beberapa rusuknya. bangun ini memiliki simetri lipat, simetri putar dan sumbu simetri {| class="wikitable" |+ |- ! bangun datar !! simetri lipat !! simetri putar !! sumbu simetri |- | persegi || 4 || 4 || 4 |- | segi-n || || || |- | persegi panjang || 2 || 2 || 2 |- | segitiga sama sisi || 3 || 3 || 3 |- | segitiga sama kaki || 1 || 0 || 1 |- | segitiga siku-siku || 1 || 0 || 1 |- | lingkaran || takhingga || takhingga || takhingga |- | jajar genjang || 0 || 2 || 0 |- | belah ketupat || 2 || 2 || 2 |- | trapesium sama kaki || 1 || 0 || 1 |- | trapesium siku-siku || 0 || 0 || 0 |- | layang-layang || 1 || 0 || 1 |- | elips || 2 || 0 || 2 |} ; Besar sudut keliling dan sudut pusat : sudut pusat = 2 x sudut keliling ; Hubungan ketiga sisi segitiga dengan jari-jari lingkaran (lingkaran dalam segitiga siku-siku): <math>r = \frac{a+b-c}{2}</math> <div class="toccolours mw-collapsible mw-collapsed" style="width:550px"><div style="font-weight:bold;line-height:1.6;">Pembuktian</div> <div class="mw-collapsible-content"> <math display="block"> \begin{align} a-r + b-r &= c \\ a+b-2r &= c \\ 2r &= a+b-c \\ r &= \frac{a+b-c}{2} \\ \end{align} </math> </div></div> ; Hubungan dua tali busur dengan jari-jari lingkaran: <math>r = \sqrt{\frac{a^2 + b^2 + c^2 + d^2}{4}}</math> <div class="toccolours mw-collapsible mw-collapsed" style="width:550px"><div style="font-weight:bold;line-height:1.6;">Pembuktian</div> <div class="mw-collapsible-content"> <math display="block"> \begin{align} \text{ misalkan } p &= \frac{c+d}{2} \text{ dan } q = \frac{a+b}{2} \\ \text{ misalkan persegi panjang dibuat x dan y} & \\ x + p &= d \\ x + \frac{c+d}{2} &= d \\ x &= d - \frac{c+d}{2} \\ x &= \frac{d-c}{2} \\ y + q &= b \\ y + \frac{a+b}{2} &= b \\ y &= b - \frac{a+b}{2} \\ y &= \frac{b-a}{2} \\ y^2 + p^2 &= r^2 \\ (\frac{b-a}{2})^2 + (\frac{c+d}{2})^2 &= r^2 \\ \frac{a^2-2ab+b^2}{4} + \frac{c^2+2cd+d^2}{4} &= r^2 \\ x^2 + q^2 &= r^2 \\ (\frac{d-c}{2})^2 + (\frac{a+b}{2})^2 &= r^2 \\ \frac{c^2-2cd+d^2}{4} + \frac{a^2+2ab+b^2}{4} &= r^2 \\ \text {jumlah dua persamaan tersebut menjadi } & \\ \frac{a^2-2ab+b^2}{4} + \frac{c^2+2cd+d^2}{4} + \frac{c^2-2cd+d^2}{4} + \frac{a^2+2ab+b^2}{4} &= 2r^2 \\ \frac{2a^2+2b^2+2c^2+2d^2}{4} &= 2r^2 \\ \frac{2(a^2+b^2+c^2+d^2)}{4} &= 2r^2 \\ \frac{a^2+b^2+c^2+d^2}{4} &= r^2 \\ a^2+b^2+c^2+d^2 &= 4r^2 \\ r &= \sqrt{\frac{a^2 + b^2 + c^2 + d^2}{4}} \\ \end{align} </math> </div></div> ; Lingkaran dalam segitiga: <math>r = \frac{L}{s}</math> (s adalah setengah keliling segitiga) <div class="toccolours mw-collapsible mw-collapsed" style="width:550px"><div style="font-weight:bold;line-height:1.6;">Pembuktian</div> <div class="mw-collapsible-content"> <math display="block"> \begin{align} \text{ misalkan luas segitiga AOC } L_a &= \frac{ra}{2} \\ \text{ misalkan luas segitiga COB } L_b &= \frac{rb}{2} \\ \text{ misalkan luas segitiga BOC } L_c &= \frac{rc}{2} \\ \text{ maka total luas ketiga segitiga tersebut adalah } L &= L_a + L_b + L_c \\ &= \frac{ra}{2} + \frac{rb}{2} + \frac{rc}{2} \\ &= r \frac{a+b+c}{2} \\ &= r s \\ r &= \frac{L}{s} \\ \end{align} </math> </div></div> ; Lingkaran luar segitiga: <math>r = \frac{abc}{4L}</math> <div class="toccolours mw-collapsible mw-collapsed" style="width:550px"><div style="font-weight:bold;line-height:1.6;">Pembuktian</div> <div class="mw-collapsible-content"> <math display="block"> \begin{align} \text{ lihat posisi kesebangunan } \frac{t}{b} &= \frac{c}{2r} \\ t &= \frac{bc}{2r} \\ L &= \frac{at}{2} \\ &= \frac{abc}{2(2r)} \\ r &= \frac{abc}{4L} \\ \end{align} </math> </div></div> ; Garis singgung (satu) lingkaran: <math>d = \sqrt{a^2-b^2}</math> ; Garis singgung persekutuan dalam (dua) lingkaran: <math>d = \sqrt{p^2-(R+r)^2}</math> ; Garis singgung persekutuan luar (dua) lingkaran: <math>d = \sqrt{p^2-(R-r)^2}</math> keterangan: : d = panjang singgung persekutuan dalam/luar lingkaran : p = jarak kedua titik pusat lingkaran ; Teorema Ceva: AF x BD x CE = BF x CD x AE ; Teorema de Pitot: AB + DC = AD + BC (segiempat luar lingkaran) ; Teorema Power de Point: (segiempat dalam lingkaran) :: AE x EC = BE x ED ; Tali busur pada satu titik di luar lingkaran: :: AB<sup>2</sup> = AD x AE :: AB x AC = AD x AE ; Teorema Ptolomeos: (segiempat dalam lingkaran) :: AC x BD = AB x DC + AD x BC ; Titik E adalah pertemuan kedua perpanjangan tali busur yang bertemu. :: maka sudut E = 1/2 (sudut besar-sudut kecil) ; Hubungan besar sudut, luas juring dan panjang busur : <math>\frac{\text{besar sudut AOB }}{\text{besar sudut COD }} = \frac{\text{luas juring AOB }}{\text{luas juring COD }} = \frac{\text{panjang busur AB }}{\text{panjang busur CD }}</math> [[Kategori:Soal-Soal Matematika]] 4pkl1w9vwq0ftrcwi8tbrzox5njpcih Resep:Ayam bumbu rujak 100 25879 108315 108213 2025-07-07T01:42:05Z Priskamarsila29 41562 Memperbaiki tulisan yang salah ketik 108315 wikitext text/x-wiki [[Berkas:Ayam bumbu rujak.jpg|jmpl|Ayam bumbu rujak]] '''Ayam bumbu rujak''' adalah sebuah makanan khas [[Jawa]] yang terbuat dari daging ayam yang masih muda dan dibumbui bumbu merah halus. Sajian ayam ini disebut bumbu rujak karena terdapat banyak [[rempah-rempah]] khas rujak, seperti cabai dan gula jawa yang umum dipakai dalam saus rujak buah.<ref>Kementerian Pertanian. 1967. ''Mustikarasa: Buku Masakan Indonesia.'' Jakarta: Kementerian Pertanian</ref> == Bahan == * 1 ekor ayam == Bumbu == * 6 siung bawang merah * 5 siung bawang putih * 10 buah cabai merah * 5 butir kemiri * 1 ruas jari kunyit * 1 potong jahe * 1 batang serai * 4 sdm minyak goreng * 4 gelas santan * 1/2 sdm air asam jawa * 2 lembar daun salam * 2 lembar daun jeruk * gula merah dan garam secukupnya == Cara Membuat == # Bersihkan dan potong ayam menjadi 10 bagian atau sesuai keinginan. # Lumuri ayam dengan air asam jawa dan 1 sdt garam. Marinasi dan diamkan sekitar 20 menit. # Haluskan bawang merah, bawang putih, cabai merah, kunyit, dan kemiri. # Tumis bumbu halus. Lalu, tambahkan daun salam, daun jeruk, serai, dan jahe. # Tambahkan garam dan gula merah secukupnya, lalu aduk hingga merata # Masukkan daging ayam yang sudah dipotong dan tambahkan santan. # Masak dengan api sedang. Aduk supaya santan tidak pecah sampai potongan daging matang dan empuk. # Hidangkan ayam bumbu rujak selagi hangat. == Referensi == <references /> [[Kategori:WikiCitaRasa]] [[Kategori:WikiCitaRasa-Bandung]] [[Kategori:Masakan Jawa]] kapek149syvseecpgxm5tamrrdxu4us Pengguna:Mistsplitter Reforged 2 25909 108316 2025-07-07T04:24:47Z Mistsplitter Reforged 41544 ←Membuat halaman berisi '{{Pp-template|Semi=yes|expired= 1 febuary 999999}} {{pp-vandalism|small=yes}} == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{Pengguna Twinkle}} {{Pengguna terkonfirmasi otomatis}} {{Pengguna perhitungan tanggal|subyek=Norges|predikat= Dette landet har vært uavhengig i|year=1814|month=5|day=17}} {{Pengguna perhitungan tanggal|subyek=The state of the earth and the universe 13.9 billion years ago|year=13900000000|month=1|day=1}} {{Pengguna perhitunga...' 108316 wikitext text/x-wiki {{Pp-template|Semi=yes|expired= 1 febuary 999999}} {{pp-vandalism|small=yes}} == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ 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indigo]] ]] |- |{{purge|[ Slett denne hurtigbufferen ]}} |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:en:User:Mistsplitter_Reforged|Halaman Inggris]] |- |[[:de:Benutzer:Mistsplitter_Reforged|Halaman Jerman]] |- |[[:fi:Käyttäjä:Mistsplitter_Reforged|Halaman Finlandia]] |- |[[:da:Bruger:Mistsplitter_Reforged|Halaman Denmark]] |- |[[:is:Notandi:Mistsplitter_Reforged|Halaman Islandia]] |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) |- |[[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) |- |} == Referensi == {{Halaman pengguna tak terlindungi}} {{Halaman pengguna tak terlindungi|2=expired= 1 febuary 9999999999999998|Semi=yes}} {{Autoconfirmed topicon}} {{Twinkle topicon}} __NOGLOBAL__ __NOGLOBAL__ Nunoguevara 4mpfeyx6azx34l6x0syrwnv6t7oj5v4 108317 108316 2025-07-07T04:27:31Z Mistsplitter Reforged 41544 Perubahan 108317 wikitext text/x-wiki == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{Pengguna Wikipedia bahasa|fr|Wikipedia bahasa Prancis}}{{Pengguna Wikipedia bahasa|nl|Wikipedia bahasa Belanda}} {{Pengguna Wikipedia bahasa|hr|Wikipedia bahasa Kroasia}} {{Pengguna Wikipedia bahasa|he|Wikipedia bahasa Ibrani}} {{Pengguna Wikipedia bahasa|ja|Wikipedia bahasa Jepang}} {{Pengguna Wikipedia bahasa|is|Wikipedia bahasa Islandia}} {{Pengguna Wikipedia bahasa|da|Wikipedia bahasa Denmark}} {{Pengguna Wikipedia bahasa|zh|Wikipedia bahasa China}} {{Pengguna Wikipedia bahasa|de|Wikipedia bahasa Jerman}} {{Pengguna Wikipedia bahasa|en|Wikipedia bahasa Inggris}} {{Purge}} {{end-col}} {{#babel:plain=1|id-n|en-5|no-3|da-3|jv-1|ar-1|nl-1|fr-1|he-0|ja-0|hr-0|zh-0}} {{Userpage}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {| |- |[[Berkas:Lactarius indigo 48568 edit.jpg|jmpl|[[Lactarius indigo]] ]] |- |{{purge|[ Slett denne hurtigbufferen 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[[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {| |- |[[Berkas:Lactarius indigo 48568 edit.jpg|jmpl|[[Lactarius indigo]] ]] |- |{{purge|[ Slett denne hurtigbufferen ]}} |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:en:User:Mistsplitter_Reforged|Halaman Inggris]] |- |[[:de:Benutzer:Mistsplitter_Reforged|Halaman Jerman]] |- |[[:fi:Käyttäjä:Mistsplitter_Reforged|Halaman Finlandia]] |- |[[:da:Bruger:Mistsplitter_Reforged|Halaman Denmark]] |- |[[:is:Notandi:Mistsplitter_Reforged|Halaman Islandia]] |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) |- |[[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) |- |} == Referensi == [[User:Nunoguevara]] __NOGLOBAL__ __NOGLOBAL__ liqqk9ixgy4c4xdxjpra6b4f9uxyx75 108319 108318 2025-07-07T04:35:37Z Mistsplitter Reforged 41544 108319 wikitext text/x-wiki == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{end-col}}{{Interproyek|* [[:w:Mistsplitter Reforged|Wikipedia]] * [[:wikt:Mistsplitter Reforged|Wiktionary]] * [[:b:Halaman Utama|Wikibooks]] * [[:q:Halaman Utama|Wikiquote]] * [[:s:Halaman Utama|Wikisource]]}}{{#babel:plain=1|id-n|en-5|no-3|da-3|jv-1|ar-1|nl-1|fr-1|he-0|ja-0|hr-0|zh-0}} {{Purge|Buat akun}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {| |- |[[Berkas:Lactarius indigo 48568 edit.jpg|jmpl|[[Lactarius indigo]] ]] |- |{{purge|[ Slett denne hurtigbufferen ]}} |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:en:User:Mistsplitter_Reforged|Halaman Inggris]] |- |[[:de:Benutzer:Mistsplitter_Reforged|Halaman Jerman]] |- |[[:fi:Käyttäjä:Mistsplitter_Reforged|Halaman Finlandia]] |- |[[:da:Bruger:Mistsplitter_Reforged|Halaman Denmark]] |- |[[:is:Notandi:Mistsplitter_Reforged|Halaman Islandia]] |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) |- |[[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) |- |} == Referensi == [[User:Nunoguevara]] __NOGLOBAL__ __NOGLOBAL__ d44r9fwda6frpfza004ran8qd37rp7z 108320 108319 2025-07-07T09:22:30Z Mistsplitter Reforged 41544 108320 wikitext text/x-wiki == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{end-col}}{{Interproyek|* [[:w:user:Mistsplitter Reforged|Wikipedia]] * [[:wikt:user:Mistsplitter Reforged|Wiktionary]] * [[:b:user:Mistsplitter Reforged|Wikibooks]] * [[:q:user:Mistsplitter Reforged|Wikiquote]] * [[:s:user:Mistsplitter Reforged|Wikisource]]}}{{#babel:plain=1|id-n|en-5|no-3|da-3|jv-1|ar-1|nl-1|fr-1|he-0|ja-0|hr-0|zh-0}} {{Purge|Buat akun}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {| |- |[[Berkas:Lactarius indigo 48568 edit.jpg|jmpl|[[Lactarius indigo]] ]] |- |{{purge|[ Slett denne hurtigbufferen ]}} |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:en:User:Mistsplitter_Reforged|Halaman Inggris]] |- |[[:de:Benutzer:Mistsplitter_Reforged|Halaman Jerman]] |- |[[:fi:Käyttäjä:Mistsplitter_Reforged|Halaman Finlandia]] |- |[[:da:Bruger:Mistsplitter_Reforged|Halaman Denmark]] |- |[[:is:Notandi:Mistsplitter_Reforged|Halaman Islandia]] |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) |- |[[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) |- |} == Referensi == [[User:Nunoguevara]] __NOGLOBAL__ __NOGLOBAL__ 9hcokt1ctr8ydhkjok5ahlxifn7iljv 108321 108320 2025-07-07T09:25:57Z Mistsplitter Reforged 41544 108321 wikitext text/x-wiki == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{Interproyek|* [[:w:user:Mistsplitter Reforged|Wikipedia]] * [[:wikt:user:Mistsplitter Reforged|Wiktionary]] * [[mw:user:Mistsplitter Reforged|Mediawiki]] * [[:b:user:Mistsplitter Reforged|Wikibooks]] * [[:q:user:Mistsplitter Reforged|Wikiquote]] * [[:s:user:Mistsplitter Reforged|Wikisource]]}} {{#babel:plain=1|id-n|en-5|no-3|da-3|jv-1|ar-1|nl-1|fr-1|he-0|ja-0|hr-0|zh-0}} {{Purge|Buat akun}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {| |- |[[Berkas:Lactarius indigo 48568 edit.jpg|jmpl|[[Lactarius indigo]] ]] |- |{{purge|[ Slett denne hurtigbufferen ]}} |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:en:User:Mistsplitter_Reforged|Halaman Inggris]] |- |[[:de:Benutzer:Mistsplitter_Reforged|Halaman Jerman]] |- |[[:fi:Käyttäjä:Mistsplitter_Reforged|Halaman Finlandia]] |- |[[:da:Bruger:Mistsplitter_Reforged|Halaman Denmark]] |- |[[:is:Notandi:Mistsplitter_Reforged|Halaman Islandia]] |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) |- |[[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) |- |} {{end-col}} == Referensi == [[User:Nunoguevara]] __NOGLOBAL__ __NOGLOBAL__ ceg22c1oitkut4wqz4ic6yrvykapr6e 108322 108321 2025-07-07T09:32:57Z Mistsplitter Reforged 41544 108322 wikitext text/x-wiki == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} [[Bruker:Mistsplitter Reforged]] {{end-col}} {{Interproyek|* [[:w:user:Mistsplitter Reforged|Wikipedia]] * [[:wikt:user:Mistsplitter Reforged|Wiktionary]] * [[mw:user:Mistsplitter Reforged|Mediawiki]] * [[:b:user:Mistsplitter Reforged|Wikibooks]] * [[:q:user:Mistsplitter Reforged|Wikiquote]] * [[:s:user:Mistsplitter Reforged|Wikisource]]}} {{#babel:plain=1|id-n|en-5|no-3|da-3|jv-1|ar-1|nl-1|fr-1|he-0|ja-0|hr-0|zh-0}} {{Purge|Buat akun}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {| |- |[[Berkas:Lactarius indigo 48568 edit.jpg|jmpl|[[Lactarius indigo]] ]] |- |{{purge|[ Slett denne hurtigbufferen ]}} |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:en:User:Mistsplitter_Reforged|Halaman Inggris]] |- |[[:de:Benutzer:Mistsplitter_Reforged|Halaman Jerman]] |- |[[:fi:Käyttäjä:Mistsplitter_Reforged|Halaman Finlandia]] |- |[[:da:Bruger:Mistsplitter_Reforged|Halaman Denmark]] |- |[[:is:Notandi:Mistsplitter_Reforged|Halaman Islandia]] |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) |- |[[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) |- |} == Referensi == [[User:Nunoguevara]] __NOGLOBAL__ __NOGLOBAL__ 9eak1l5g9aot3eo5omhyqaalm54y86k 108323 108322 2025-07-07T09:37:35Z Mistsplitter Reforged 41544 108323 wikitext text/x-wiki == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{end-col}} {{Interproyek|* [[:w:user:Mistsplitter Reforged|Wikipedia]] * [[:wikt:user:Mistsplitter Reforged|Wiktionary]] * [[mw:user:Mistsplitter Reforged|Mediawiki]] * [[:b:user:Mistsplitter Reforged|Wikibooks]] * [[:q:user:Mistsplitter Reforged|Wikiquote]] * [[:s:user:Mistsplitter Reforged|Wikisource]]}} {{#babel:plain=1|id-n|en-5|no-3|da-3|jv-1|ar-1|nl-1|fr-1|he-0|ja-0|hr-0|zh-0}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {| |- |[[Berkas:Lactarius indigo 48568 edit.jpg|jmpl|[[Lactarius indigo]] ]] |- |{{purge|[ Slett denne hurtigbufferen ]}} |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:en:User:Mistsplitter_Reforged|Halaman Inggris]] |- |[[:de:Benutzer:Mistsplitter_Reforged|Halaman Jerman]] |- |[[:fi:Käyttäjä:Mistsplitter_Reforged|Halaman Finlandia]] |- |[[:da:Bruger:Mistsplitter_Reforged|Halaman Denmark]] |- |[[:is:Notandi:Mistsplitter_Reforged|Halaman Islandia]] |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) |- |[[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) |- |} {{Purge|Buat akun}} == Referensi == [[User:Nunoguevara]] __NOGLOBAL__ __NOGLOBAL__ gn7h3ajal6yexqwft3be8w8ooelc66i 108324 108323 2025-07-07T09:38:46Z Mistsplitter Reforged 41544 108324 wikitext text/x-wiki == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{end-col}} {{#babel:plain=1|id-n|en-5|no-3|da-3|jv-1|ar-1|nl-1|fr-1|he-0|ja-0|hr-0|zh-0}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {{Interproyek| * [[:w:user:Mistsplitter Reforged|Wikipedia]] * [[:wikt:user:Mistsplitter Reforged|Wiktionary]] * [[mw:user:Mistsplitter Reforged|Mediawiki]] * [[:b:user:Mistsplitter Reforged|Wikibooks]] * [[:q:user:Mistsplitter Reforged|Wikiquote]] * [[:s:user:Mistsplitter Reforged|Wikisource]]}} {| |- |[[Berkas:Lactarius indigo 48568 edit.jpg|jmpl|[[Lactarius indigo]] ]] |- |{{purge|[ Slett denne hurtigbufferen ]}} |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:en:User:Mistsplitter_Reforged|Halaman Inggris]] |- |[[:de:Benutzer:Mistsplitter_Reforged|Halaman Jerman]] |- |[[:fi:Käyttäjä:Mistsplitter_Reforged|Halaman Finlandia]] |- |[[:da:Bruger:Mistsplitter_Reforged|Halaman Denmark]] |- |[[:is:Notandi:Mistsplitter_Reforged|Halaman Islandia]] |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) |- |[[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) |- |} {{Purge|Buat akun}} == Referensi == [[User:Nunoguevara]] __NOGLOBAL__ __NOGLOBAL__ kettnechaq8besr496a9lfshdnfdqw1 108325 108324 2025-07-07T09:40:45Z Mistsplitter Reforged 41544 /* Lihat pula */ 108325 wikitext text/x-wiki == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{end-col}} {{#babel:plain=1|id-n|en-5|no-3|da-3|jv-1|ar-1|nl-1|fr-1|he-0|ja-0|hr-0|zh-0}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {{Interproyek|* [[:w:user:Mistsplitter Reforged|Wikipedia]] * [[:wikt:user:Mistsplitter Reforged|Wiktionary]] * [[mw:user:Mistsplitter Reforged|Mediawiki]] * [[:b:user:Mistsplitter Reforged|Wikibooks]] * [[:q:user:Mistsplitter Reforged|Wikiquote]] * [[:s:user:Mistsplitter Reforged|Wikisource]]}} {{Interproyek|* [[:w:user:Mistsplitter Reforged|Wikipedia]] * [[:wikt:user:Mistsplitter Reforged|Wiktionary]] * [[mw:user:Mistsplitter Reforged|Mediawiki]] * [[:b:user:Mistsplitter Reforged|Wikibooks]] * [[:q:user:Mistsplitter Reforged|Wikiquote]] * [[:s:user:Mistsplitter Reforged|Wikisource]]}} {| |- |[[Berkas:Lactarius indigo 48568 edit.jpg|jmpl|[[Lactarius indigo]] ]] |- |{{purge|[ Slett denne hurtigbufferen ]}} |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:en:User:Mistsplitter_Reforged|Halaman Inggris]] |- |[[:de:Benutzer:Mistsplitter_Reforged|Halaman Jerman]] |- |[[:fi:Käyttäjä:Mistsplitter_Reforged|Halaman Finlandia]] |- |[[:da:Bruger:Mistsplitter_Reforged|Halaman Denmark]] |- |[[:is:Notandi:Mistsplitter_Reforged|Halaman Islandia]] |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) |- |[[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) |- |} {{Purge|Buat akun}} == Referensi == [[User:Nunoguevara]] __NOGLOBAL__ __NOGLOBAL__ gzg654v268xg776fexiuabnzd1bqv4f 108326 108325 2025-07-07T09:52:31Z Mistsplitter Reforged 41544 108326 wikitext text/x-wiki == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{end-col}} {{#babel:plain=1|id-n|en-5|no-3|da-3|jv-1|ar-1|nl-1|fr-1|he-0|ja-0|hr-0|zh-0}} [[Berkas:Mandelbrot sequence new.gif|pus|jmpl|320x320px]] {{Pp-protected|small=yes|expiry=1 april 999999|demolevel=sysop=full|demospace=sysop=full}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {{Interproyek|* [[:w:user:Mistsplitter Reforged|Wikipedia]] * [[:wikt:user:Mistsplitter Reforged|Wiktionary]] * [[mw:user:Mistsplitter Reforged|Mediawiki]] * [[:b:user:Mistsplitter Reforged|Wikibooks]] * [[:q:user:Mistsplitter Reforged|Wikiquote]] * [[:s:user:Mistsplitter Reforged|Wikisource]]}} {{Interproyek|* [[:w:user:Mistsplitter Reforged|Wikipedia]] * [[:wikt:user:Mistsplitter Reforged|Wiktionary]] * [[mw:user:Mistsplitter Reforged|Mediawiki]] * [[:b:user:Mistsplitter Reforged|Wikibooks]] * [[:q:user:Mistsplitter Reforged|Wikiquote]] * [[:s:user:Mistsplitter Reforged|Wikisource]]}} {| |- |[[Berkas:Lactarius indigo 48568 edit.jpg|jmpl|[[Lactarius indigo]] ]] |- |{{purge|[ Slett denne hurtigbufferen ]}} |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:en:User:Mistsplitter_Reforged|Halaman Inggris]] |- |[[:de:Benutzer:Mistsplitter_Reforged|Halaman Jerman]] |- |[[:fi:Käyttäjä:Mistsplitter_Reforged|Halaman Finlandia]] |- |[[:da:Bruger:Mistsplitter_Reforged|Halaman Denmark]] |- |[[:is:Notandi:Mistsplitter_Reforged|Halaman Islandia]] |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) |- |[[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) |- |} {{Purge|Buat akun}} == Referensi == [[User:Nunoguevara]] __NOGLOBAL__ __NOGLOBAL__ rtio9l9fmz0sivdto8fmxzssuazernh 108327 108326 2025-07-07T09:53:28Z Mistsplitter Reforged 41544 /* Lihat pula */ 108327 wikitext text/x-wiki == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{end-col}} {{#babel:plain=1|id-n|en-5|no-3|da-3|jv-1|ar-1|nl-1|fr-1|he-0|ja-0|hr-0|zh-0}} [[Berkas:Mandelbrot sequence new.gif|pus|jmpl|320x320px]] {{Pp-protected|small=yes|expiry=1 april 999999|demolevel=sysop=full|demospace=sysop=full}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {{Interproyek|* [[:w:user:Mistsplitter Reforged|Wikipedia]] * [[:wikt:user:Mistsplitter Reforged|Wiktionary]] * [[mw:user:Mistsplitter Reforged|Mediawiki]] * [[:b:user:Mistsplitter Reforged|Wikibooks]] * [[:q:user:Mistsplitter Reforged|Wikiquote]] * [[:s:user:Mistsplitter Reforged|Wikisource]]}} {{Interproyek|* [[:w:user:Mistsplitter Reforged|Wikipedia]] * [[:wikt:user:Mistsplitter Reforged|Wiktionary]] * [[mw:user:Mistsplitter Reforged|Mediawiki]] * [[:b:user:Mistsplitter Reforged|Wikibooks]] * [[:q:user:Mistsplitter Reforged|Wikiquote]] * [[:s:user:Mistsplitter Reforged|Wikisource]]}} {| |- | |- |{{purge|[ Slett denne hurtigbufferen ]}} |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:en:User:Mistsplitter_Reforged|Halaman Inggris]] |- |[[:de:Benutzer:Mistsplitter_Reforged|Halaman Jerman]] |- |[[:fi:Käyttäjä:Mistsplitter_Reforged|Halaman Finlandia]] |- |[[:da:Bruger:Mistsplitter_Reforged|Halaman Denmark]] |- |[[:is:Notandi:Mistsplitter_Reforged|Halaman Islandia]] |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) |- |[[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) |- |} {{Purge|Buat akun}} == Referensi == [[User:Nunoguevara]] __NOGLOBAL__ __NOGLOBAL__ npm4u2bibekrlbzimtma6gbehebd7k5 108329 108327 2025-07-07T09:59:04Z Mistsplitter Reforged 41544 108329 wikitext text/x-wiki == Profil == {{Interproyek|* [[:w:user:Mistsplitter Reforged|Wikipedia]] * [[:wikt:user:Mistsplitter Reforged|Wiktionary]] * [[mw:user:Mistsplitter Reforged|Mediawiki]] * [[:b:user:Mistsplitter Reforged|Wikibooks]] * [[:q:user:Mistsplitter Reforged|Wikiquote]] * [[:s:user:Mistsplitter Reforged|Wikisource]]}} {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{end-col}} {{#babel:plain=1|id-n|en-5|no-3|da-3|jv-1|ar-1|nl-1|fr-1|he-0|ja-0|hr-0|zh-0}} {{Pp-protected|small=yes|expiry=1 april 999999|demolevel=sysop=full|demospace=sysop=full}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {| |- | |- |{{purge|[ Slett denne hurtigbufferen ]}} |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:en:User:Mistsplitter_Reforged|Halaman Inggris]] |- |[[:de:Benutzer:Mistsplitter_Reforged|Halaman Jerman]] |- |[[:fi:Käyttäjä:Mistsplitter_Reforged|Halaman Finlandia]] |- |[[:da:Bruger:Mistsplitter_Reforged|Halaman Denmark]] |- |[[:is:Notandi:Mistsplitter_Reforged|Halaman Islandia]] |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) |- |[[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) |- |} {{Purge|Buat akun}} == Referensi == [[User:Nunoguevara]] __NOGLOBAL__ __NOGLOBAL__ dbvxxpaurexhjzd9xc65w0bowf3ya2v 108332 108329 2025-07-07T10:21:22Z Mistsplitter Reforged 41544 108332 wikitext text/x-wiki == Profil == {{Interproyek|* [[:w:user:Mistsplitter Reforged|Wikipedia]] * [[:wikt:user:Mistsplitter Reforged|Wiktionary]] * [[mw:user:Mistsplitter Reforged|Mediawiki]] * [[:b:user:Mistsplitter Reforged|Wikibooks]] * [[:q:user:Mistsplitter Reforged|Wikiquote]] * [[:s:user:Mistsplitter Reforged|Wikisource]]}} {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{end-col}} {{#babel:plain=1|id-n|en-5|no-3|da-3}} {{Pp-protected|small=yes|expiry=1 april 999999|demolevel=sysop=full|demospace=sysop=full}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {| |- | |- |{{purge|[ Slett denne hurtigbufferen ]}} |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:en:User:Mistsplitter_Reforged|Halaman Inggris]] |- |[[:de:Benutzer:Mistsplitter_Reforged|Halaman Jerman]] |- |[[:fi:Käyttäjä:Mistsplitter_Reforged|Halaman Finlandia]] |- |[[:da:Bruger:Mistsplitter_Reforged|Halaman Denmark]] |- |[[:is:Notandi:Mistsplitter_Reforged|Halaman Islandia]] |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) |- |[[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) |- |} {{Purge|Buat akun}} == Referensi == [[User:Nunoguevara]] [[no:User:mistsplitter Reforged]] __NOGLOBAL__ __NOGLOBAL__ igx6imf2l0kkkbrb7wqzz9xw1u6137g 108333 108332 2025-07-07T10:26:02Z Mistsplitter Reforged 41544 108333 wikitext text/x-wiki == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{end-col}} {{#babel:plain=1|id-n|en-5|no-3|da-3}} {{Pp-protected|small=yes|expiry=1 april 999999|demolevel=sysop=full|demospace=sysop=full}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {| |- | |- |{{purge|[ Slett denne hurtigbufferen ]}} |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:en:User:Mistsplitter_Reforged|Halaman Inggris]] |- |[[:de:Benutzer:Mistsplitter_Reforged|Halaman Jerman]] |- |[[:fi:Käyttäjä:Mistsplitter_Reforged|Halaman Finlandia]] |- |[[:da:Bruger:Mistsplitter_Reforged|Halaman Denmark]] |- |[[:is:Notandi:Mistsplitter_Reforged|Halaman Islandia]] |- |[[Pengguna:Mistsplitter Reforged/Bak pasir|Bak pasir pribadi]] |- |[[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) |- |[[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) |- |} == Referensi == [[User:Nunoguevara]] [[no:User:mistsplitter Reforged]] [[en:User:mistsplitter Reforged]] [[da:User:mistsplitter Reforged]] [[pl:User:mistsplitter Reforged]] [[is:User:mistsplitter Reforged]] [[es:User:mistsplitter Reforged]] [[pt:User:mistsplitter Reforged]] [[fr:User:mistsplitter Reforged]] __NOGLOBAL__ __NOGLOBAL__ smkkb3u88x9bwk1rwcw7frmefc24rtr 108334 108333 2025-07-07T10:28:45Z Mistsplitter Reforged 41544 /* Lihat pula */ 108334 wikitext text/x-wiki == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{end-col}} {{#babel:plain=1|id-n|en-5|no-3|da-3}} {{Pp-protected|small=yes|expiry=1 april 999999|demolevel=sysop=full|demospace=sysop=full}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {| |- | |- |{{purge|[ Slett denne hurtigbufferen ]}} |- |[[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) |- |[[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) |- |} == Referensi == [[User:Nunoguevara]] [[no:User:mistsplitter Reforged]] [[en:User:mistsplitter Reforged]] [[da:User:mistsplitter Reforged]] [[pl:User:mistsplitter Reforged]] [[is:User:mistsplitter Reforged]] [[es:User:mistsplitter Reforged]] [[pt:User:mistsplitter Reforged]] [[fr:User:mistsplitter Reforged]] __NOGLOBAL__ __NOGLOBAL__ qsszi4mgwtdgw9930illkj8qo53hnxz 108335 108334 2025-07-07T10:30:36Z Mistsplitter Reforged 41544 108335 wikitext text/x-wiki == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{end-col}} {{#babel:plain=1|id-n|en-5|no-3|da-3}} {{Pp-protected|small=yes|expiry=1 april 999999|demolevel=sysop=full|demospace=sysop=full}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {{purge|[ Slett denne hurtigbufferen ]}} [[:he:משתמש:Mistsplitter_Reforged/טיוטה|Bak pasir pribadi]] ([[Israel|Ibrani]]) [[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) == Referensi == [[User:Nunoguevara]] [[no:User:mistsplitter Reforged]] [[en:User:mistsplitter Reforged]] [[da:User:mistsplitter Reforged]] [[pl:User:mistsplitter Reforged]] [[is:User:mistsplitter Reforged]] [[es:User:mistsplitter Reforged]] [[pt:User:mistsplitter Reforged]] [[fr:User:mistsplitter Reforged]] [[sv:User:mistsplitter Reforged]] [[fi:User:mistsplitter Reforged]] [[ar:User:mistsplitter Reforged]] [[nn:User:mistsplitter Reforged]] [[zh:User:mistsplitter Reforged]] [[ja:User:mistsplitter Reforged]] __NOGLOBAL__ __NOGLOBAL__ si3clh1ej6hyd5z6hjqkbgpl02udq2o 108336 108335 2025-07-07T10:32:08Z Mistsplitter Reforged 41544 108336 wikitext text/x-wiki == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{end-col}} {{#babel:plain=1|id-n|en-5|no-3|da-3}} {{Pp-protected|small=yes|expiry=1 april 999999|demolevel=sysop=full|demospace=sysop=full}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {{purge|[ Slett denne hurtigbufferen ]}} [[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) == Referensi == [[User:Nunoguevara]] [[no:User:mistsplitter Reforged]] [[en:User:mistsplitter Reforged]] [[da:User:mistsplitter Reforged]] [[pl:User:mistsplitter Reforged]] [[is:User:mistsplitter Reforged]] [[es:User:mistsplitter Reforged]] [[pt:User:mistsplitter Reforged]] [[fr:User:mistsplitter Reforged]] [[sv:User:mistsplitter Reforged]] [[fi:User:mistsplitter Reforged]] [[ar:User:mistsplitter Reforged]] [[nn:User:mistsplitter Reforged]] [[zh:User:mistsplitter Reforged]] [[ja:User:mistsplitter Reforged]] __NOGLOBAL__ __NOGLOBAL__ nrlxpmdrio1xnbc8a4woczyhrjjmdfy 108337 108336 2025-07-07T10:32:33Z Mistsplitter Reforged 41544 /* Referensi */ 108337 wikitext text/x-wiki == Profil == {{purge|[ OPPRETT ARTIKKEL NÅ ] }} {{col}} {{end-col}} {{#babel:plain=1|id-n|en-5|no-3|da-3}} {{Pp-protected|small=yes|expiry=1 april 999999|demolevel=sysop=full|demospace=sysop=full}} == Lihat pula == [[Berkas:New-Bouncywikilogo.gif|jmpl|101x101px]] [[Berkas:New-Bouncywikilogo.gif|jmpl|100x100px]] {{purge|[ Slett denne hurtigbufferen ]}} [[mediawikiwiki:User:Mistsplitter_Reforged|Halaman Inggris]] ([[MediaWiki|Mediawiki]]) == Referensi == [[User:Nunoguevara]] [[no:User:mistsplitter Reforged]] [[en:User:mistsplitter Reforged]] [[da:User:mistsplitter Reforged]] [[pl:User:mistsplitter Reforged]] [[is:User:mistsplitter Reforged]] [[es:User:mistsplitter Reforged]] [[pt:User:mistsplitter Reforged]] [[fr:User:mistsplitter Reforged]] [[sv:User:mistsplitter Reforged]] [[fi:User:mistsplitter Reforged]] [[ar:User:mistsplitter Reforged]] [[nn:User:mistsplitter Reforged]] [[zh:User:mistsplitter Reforged]] [[ja:User:mistsplitter Reforged]] [[he:User:mistsplitter Reforged]] __NOGLOBAL__ __NOGLOBAL__ 13q227ybf9d954fsg4lgzfsqikkqc2n