Chapter 4 - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 368: 77

$x=\sqrt{5}$

$\displaystyle \frac{1}{16}=\frac{1}{2^{4}}=2^{-4}$ $ 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 $5^{-1/2}=x$ $x=\sqrt{5}$