Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 405: 86

$f^{-1}(x)= \frac{10^{x}}{3}$

We are given: $f(x)=\log 3x$ To find the inverse, we switch $x$ and $y$ and solve for $y$: $y= \log 3x$ $x= \log 3y$ $10^{x}=3y$ $y=\frac{10^{x}}{3}$ Therefore: $f^{-1}(x)= \frac{10^{x}}{3}$