Answer
$f(.027)=3$
Work Step by Step
We are given that $f(x)=log_{.3}x$ and that $g(x)=.3^{x}$ is the inverse of $f(x)$. We are also told that the ordered pair (3,.027) is a solution of the function $g(x)$.
As seen in Section 9.2, when the ordered pair $(x_{1},y_{1})$ is a solution to a function, that function's inverse will have a solution of $(y_{1},x_{1})$.
Therefore, the ordered pair $(.027,3)$ will be a solution of $f(x)$. This is written in function notation as $f(.027)=3$, which tells us that $f(x)$ has a value of 3 when $x=.027$.
$f(.027)=log_{.3}.027=3$
