Question:
Solve for $x:\left(\frac{2}{5}\right)^{2 x-2}=\frac{32}{3125}$
Solution:
$\left(\frac{2}{5}\right)^{2 x-2}=\frac{32}{3125}$
$\Rightarrow\left(\frac{2}{5}\right)^{2 x-2}=\frac{2^{5}}{5^{5}}$
$\Rightarrow\left(\frac{2}{5}\right)^{2 x-2}=\left(\frac{2}{5}\right)^{5}$
$\Rightarrow 2 x-2=5$
$\Rightarrow 2 x=5+2$
$\Rightarrow x=\frac{7}{2}$
Hence, $x=\frac{7}{2}$.
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