Answer
$x=\frac{1}{9}$
Work Step by Step
If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x\gt0$ and every real number $y$.
Therefore, $log_{3}x=-2$ is equivalent to $3^{-2}=x$.
We know that $x=\frac{1}{9}$, because $3^{-2}=\frac{1}{3^{2}}=\frac{1}{3\times3}=\frac{1}{9}$.
