To find the inverse of the function \( f(x) = \log_{13}(x) \), we start by replacing \( f(x) \) with \( y \):
\[ y = \log_{13}(x) \]
Next, to find the inverse, we swap \( x \) and \( y \):
\[ x = \log_{13}(y) \]
Now, we need to solve for \( y \). We can rewrite the logarithmic equation in its exponential form:
\[ y = 13^x \]
Thus, the inverse function is:
\[ f^{-1}(x) = 13^x \]
So, the inverse of \( f(x) = \log_{13}(x) \) is \( f^{-1}(x) = 13^x \).