Question

$( \frac{1}{81})^{2x} = \frac{1}{27}$
$( \frac{9}{25})=( \frac{3}{5}) ^{3x}$
$( \frac{4}{5}) ^{2x=}1$ 
$( \frac{2}{3}) ^{x} = \frac{9}{4}$
$( \sqrt{} \frac{125}{27}) ^{x}= \frac{81}{625}$

Answer 1

$a)(\frac{1}{81})^{2x}=\frac{1}{27} \\ \\ (\frac{1}{3})^{8x}=(\frac{1}{3})^3 \rightarrow 8x=3 \rightarrow x=\frac{3}{8} \\ \\ b)(\frac{9}{25})=(\frac{3}{5})^{3x} \\ \\ (\frac{3}{5})^2=(\frac{3}{5})^{3x} \rightarrow 3x=2 \rightarrow x=\frac{2}{3} \\ \\ c) (\frac{4}{5})^{2x}=1 \\ \\ (\frac{4}{5})^{2x}=(\frac{4}{5})^0 \rightarrow 2x=0 \rightarrow x=0 \\ \\ d)(\frac{2}{3})^x=\frac{9}{4} \\ \\ (\frac{2}{3})x=(\frac{2}{3})^{-2} \rightarrow 2x=-2 \rightarrow x=-1$

$e)( \sqrt{\frac{125}{27}})^{\frac{x}{2} =\frac{81}{625} \\ (\frac{5}{3})^{\frac{x}{2}=(\frac{5}{3})^{-4} \rightarrow \frac{x}{2}=-4 \rightarrow x=-8$