Answer
$x=-2$
Work Step by Step
We are given that $3^{x}=\frac{1}{9}$. Both of these numbers are powers of 3, so we can rewrite the equation as $3^{x}=3^{-2}$.
We know that $3^{-2}=\frac{1}{3^{2}}=\frac{1}{9}$.
From the uniqueness of $b^{x}$, we know that $b^{x}=b^{y}$ is equivalent to $x=y$ (when $b\gt0$ and $b\ne1$).
Therefore, $x=-2$.
