Step 1 :Let's find the inverse of the function $f(x)=18^{x}$.
Step 2 :The inverse of a function is found by switching the x and y (or input and output) in the original function. So, if $f(x)=18^{x}$, then $f^{-1}(x)$ is found by solving the equation $x=18^{y}$ for y.
Step 3 :This can be done by taking the logarithm base 18 of both sides of the equation.
Step 4 :So, $f^{-1}(x)=\frac{\log(x)}{\log(18)}$.
Step 5 :\(\boxed{f^{-1}(x)=\frac{\log(x)}{\log(18)}}\) is the final answer.