If f(x) = 3^x, what is f^-1(81)?

The inverse of $f(x)=3^x$ is the logarithm base $3$, so $f^{-1}(81)=\log_3(81)$, which asks, what power of $3$ gives $81$? Since $3^4=81$, the answer is $4$, choice G. Equivalently, solve $f(x)=81$: $3^x=81=3^4$, so $x=4$. Choice J ($243$) is $f(5)=3^5$, a value of $f$ rather than the input. Choice H ($27$) is $81\div3$. Choice F ($3$) gives $f(3)=27$. The inverse takes an output of $f$ and returns the input that produced it.