Answer
$-2$
Work Step by Step
NOoe that $y=\log_a x \text{ is equivalent to } x= a^y$
Thus, if $y = \log_{1/3} 9$, then $\left(\dfrac{1}{3}\right)^y=9$
Since $9=3^2=\left(\dfrac{1}{3}\right)^{-2},$ then
$\left(\dfrac{1}{3}\right)^y=\left(\dfrac{1}{3}\right)^{-2}$
Use the rule $a^m=a^n \implies m=n$ to obtain:
$y=-2$
Therefore,
$ \log_{1/3} 9 = \boxed{-2}$
