Answer
$x=-2$
Work Step by Step
First, we let
$\log_{3}{\frac{1}{9}} = x$
RECALL:
$\log_b{y} =x \longrightarrow b^x=y$
Use the rule above, where $y=\frac{1}{9}$ and $b=3$, to obtain:
$3^x=\frac{1}{9}$
Write $\frac{1}{9}$ as $ 3^{-2}$ to obtain:
$3^x=3^{-2}$
Use the rule "If $a^x=a^y$, then $x=y$" to obtain:
$x=-2$
