Answer
$f^{-1}(x) = \log_3 (\frac{x}{5})$
Work Step by Step
$f(x) = 5(3)^{x}$
Let $f(x) = y$
$y = 5(3)^{x}$
Swap the variables $x$ and $y$ and then solve for $y$ to find the inverse:
$x = 5(3)^{y}$
$\frac{x}{5} = (3)^{y}$
$y = \log_3 (\frac{x}{5})$
$f^{-1}(x) = \log_3 (\frac{x}{5})$
