Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 31

$x=\dfrac{1}{16}$

In exponential form, the given logarithmic equation, $ \log_4 x =-2 ,$ is equivalent to \begin{array}{l}\require{cancel} x=4^{-2} .\end{array} Hence, the value of the variable that satisfies the given equation is \begin{array}{l}\require{cancel} x=\dfrac{1}{4^{2}} \\\\ x=\dfrac{1}{16} .\end{array}