Answer
$x=\sqrt{5}$
Work Step by Step
$\displaystyle \frac{1}{16}=\frac{1}{2^{4}}=2^{-4}$
$ 2^{2/\log_{5}x}=2^{-4}\qquad$ ... apply $\log_{2}$ on both sides
$\displaystyle \frac{2}{\log_{5}x}=-4\qquad$ ... $/\displaystyle \times\frac{\log_{5}x}{-4}$
$\displaystyle \frac{2}{-4}=\log_{5}x\qquad$ ... apply $5^{(..)}$ on both sides
$5^{-1/2}=x$
$x=\sqrt{5}$
