Chapter 4 - Section 4.3 - Logarithmic Functions - Summary Exercises on Inverse, Exponential, and Logarithmic Functions - Page 427: 32

$x=\dfrac{1}{3}$

Since $y=b^x$ is equivalent to $\log_b y=x,$ then the given equation, $ \log_x 3=-1 ,$ is equivalent to \begin{array}{l}\require{cancel} x^{-1}=3 \\\\ \dfrac{1}{x^1}=3 \\\\ \dfrac{1}{x}=3 .\end{array} Using cross-multiplication and the properties of equality, then, \begin{array}{l}\require{cancel} 1=3x \\\\ \dfrac{1}{3}=x \\\\ x=\dfrac{1}{3} .\end{array}