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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.

Explore how to find the inverse of the exponential function f(x) = a^x. This problem uses logarithmic properties to compute the inverse, a core concept for high school students learning about functions and their inverses. Perfect for Grades 10-12.

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