Nilai x yang memenuhi persamaan ![( \frac{5}{ 5^{x-3} }) ^{2} = \sqrt[3]{ \frac{1}{125} }](https://tex.z-dn.net/?f=%28+%5Cfrac%7B5%7D%7B+5%5E%7Bx-3%7D+%7D%29+%5E%7B2%7D+%3D+%5Csqrt%5B3%5D%7B+%5Cfrac%7B1%7D%7B125%7D+%7D+ "( \frac{5}{ 5^{x-3} }) ^{2} = \sqrt[3]{ \frac{1}{125} }")
adalah
ImmanuelSinaga
![$\begin{align} \left(\frac{5}{5^{x-3}}\right)^2~~&=~~\sqrt[3]{\frac{1}{125}} \\ \left(5^{4-x}\right)^2~~&=~~\sqrt[3]{5^{-3}} \\ 5^{8-2x}~~&=~~5^{-\frac{3}{3}} \\ \\ 8-2x~~&=~~-1 \\ 8+1~~&=~~2x \\ 9~~&=~~2x \\ \frac{9}{2}~~&=~~x \\ \\ \therefore~~x~=~\frac{9}{2} \end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7D+%5Cleft%28%5Cfrac%7B5%7D%7B5%5E%7Bx-3%7D%7D%5Cright%29%5E2%7E%7E%26%3D%7E%7E%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B125%7D%7D+%5C%5C+%5Cleft%285%5E%7B4-x%7D%5Cright%29%5E2%7E%7E%26%3D%7E%7E%5Csqrt%5B3%5D%7B5%5E%7B-3%7D%7D+%5C%5C+5%5E%7B8-2x%7D%7E%7E%26%3D%7E%7E5%5E%7B-%5Cfrac%7B3%7D%7B3%7D%7D+%5C%5C+%5C%5C+8-2x%7E%7E%26%3D%7E%7E-1+%5C%5C+8%2B1%7E%7E%26%3D%7E%7E2x+%5C%5C+9%7E%7E%26%3D%7E%7E2x+%5C%5C+%5Cfrac%7B9%7D%7B2%7D%7E%7E%26%3D%7E%7Ex+%5C%5C+%5C%5C+%5Ctherefore%7E%7Ex%7E%3D%7E%5Cfrac%7B9%7D%7B2%7D++%5Cend%7Balign%7D "$\begin{align} \left(\frac{5}{5^{x-3}}\right)^2~~&=~~\sqrt[3]{\frac{1}{125}} \\ \left(5^{4-x}\right)^2~~&=~~\sqrt[3]{5^{-3}} \\ 5^{8-2x}~~&=~~5^{-\frac{3}{3}} \\ \\ 8-2x~~&=~~-1 \\ 8+1~~&=~~2x \\ 9~~&=~~2x \\ \frac{9}{2}~~&=~~x \\ \\ \therefore~~x~=~\frac{9}{2} \end{align}")
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