Answer
$x=\dfrac{1}{9}$
Work Step by Step
Converting to exponential form, the solution to the given logarithmic equation, $
\log_3{x}=-2
,$ is
\begin{array}{l}\require{cancel}
x=3^{-2}
\\\\
x=\dfrac{1}{3^{2}}
\\\\
x=\dfrac{1}{9}
.\end{array}