Answer
$f^{-1}(x)=\displaystyle \frac{10^{x}}{3}$
Work Step by Step
To find the inverse of y=f(x):
1. swap x and y in the expression of the function
2. solve for y
3. replace $y $with $f^{-1}(x)$
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$y=\log 3x$
$ x=\log 3y\qquad$... apply $10^{(..)}$ to both sides
$ 10^{x}=3y\qquad$... $/\div 3$
$y=\displaystyle \frac{10^{x}}{3}$
$f^{-1}(x)=\displaystyle \frac{10^{x}}{3}$
