Answer
$x=\dfrac{1}{3}$
Work Step by Step
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}