Answer
True.
Work Step by Step
Definition of Logarithm:
For $a > 0, a\neq 1$, and $x > 0$,
$y=\log_{a}x$ means $a^{y}=x$.
$....................................$
Here, $a=3 > 0, y=-2, $and $ x=\displaystyle \frac{1}{9},$ so
$3^{-2}=\displaystyle \frac{1}{9}$ ( $a^{y}=x)$
means
$\displaystyle \log_{3}(\frac{1}{9})=-2$ $ (y=\log_{a}x).$
The statement is true.
