Answer
(a) $ -4$
(b) $ 6$
(c) $ 4$
(d) $-1$
Work Step by Step
Given $f(x)=log_ax$ and $f(3)=2$, we have $f(3)=log_a3=2$ and $a^2=3$, thus $a=3^{1/2}$.
(a) $f(\frac{1}{9})=log_{3^{1/2}}(\frac{1}{9})=log_{3^{1/2}}(3^{-2})=\frac{-2}{1/2}=-4$
(b) $f(27)=log_{3^{1/2}}(27)=log_{3^{1/2}}(3^{3})=\frac{3}{1/2}=6$
(c) $f(9)=log_{3^{1/2}}(9)=log_{3^{1/2}}(3^{2})=\frac{2}{1/2}=4$
(d) $f(\frac{\sqrt 3}{3})=log_{3^{1/2}}(\frac{\sqrt 3}{3})=log_{3^{1/2}}(3^{-1/2})=\frac{-1/2}{1/2}=-1$
