## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$-2$
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, $\log_{1/3} 9 = \boxed{-2}$