Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 32

$x=\dfrac{1}{125}$

In exponential form, the given logarithmic equation, $ \log_5 x =-3 ,$ is equivalent to \begin{array}{l}\require{cancel} x=5^{-3} .\end{array} Hence, the value of the variable that satisfies the given equation is \begin{array}{l}\require{cancel} x=\dfrac{1}{5^3} \\\\ x=\dfrac{1}{125} .\end{array}