Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 404: 77

$x=\frac{1}{\sqrt{5}}\approx 0.4472$

$2^{2/\log_{5}x}= \frac{1}{16}$ $\log_{2}(\frac{1}{16})=\frac{2}{\log_{5}x}$ $\log_{2}(2^{-4})=\frac{2}{\log_{5}x}$ $-4=\frac{2}{\log_{5}x}$ $\log_{5}x=\frac{2}{-4}=-\frac{1}{2}$ $5^{-\frac{1}{2}}=x$ $\frac{1}{5^{\frac{1}{2}}}=x$ $x=\frac{1}{\sqrt{5}}\approx 0.4472$