Answer
$-2$
Work Step by Step
Since $9=3^2$, the given expression is equivalent to:
$\log_3{(\frac{1}{3^2})}$
Using the rule $\frac{1}{a^m} = a^{-m}, a\ne0$ gives:
$\log_3{(\frac{1}{3^2})}=\log_3{(3^{-2})}$
RECALL:
$\log_a{(a^n)} = n, a \gt 0, a \ne1$
Using the property above gives:
$\log_3{(3^{-2})} = -2$
Thus, $\log_3{(\frac{1}{9})} = -2$.
