The given function is $f(x) = a^x$, and the question asks for the inverse function $f^{-1}(x)$.

To find the inverse:

1. Start by writing $y = f(x) = a^x$.
2. Swap $x$ and $y$ to reflect the inverse function: $x = a^y$
3. Solve for $y$. Take the logarithm base $a$ on both sides: $\log_a(x) = y$
4. Thus, the inverse function is: $f^{-1}(x) = \log_a(x)$

Therefore, the correct answer is:

$\boxed{\log_a x}$

Would you like more details or further clarification on this?

Here are 5 related questions to expand on this topic:

1. How do you find the inverse of a logarithmic function?
2. What is the relationship between exponential and logarithmic functions?
3. Can the base $a$ in the function $f(x) = a^x$ be any positive number?
4. How do you interpret the graph of an exponential function versus its inverse?
5. What are the key properties of the inverse of an exponential function?

Tip: Always remember that the inverse of an exponential function is a logarithmic function with the same base.