1. **Problem Statement:** Find the inverse of an exponential function, typically given as $y = a^x$ where $a > 0$ and $a \neq 1$. 2. **Formula and Important Rules:** The inverse of an exponential function is a logarithmic function. If $y = a^x$, then the inverse is $x = \log_a(y)$. 3. **Step-by-step Explanation:** - Start with the equation $y = a^x$. - To find the inverse, swap $x$ and $y$: $x = a^y$. - Solve for $y$ by taking the logarithm base $a$ of both sides: $y = \log_a(x)$. 4. **Summary:** The inverse function of $y = a^x$ is $y = \log_a(x)$. This means the logarithm base $a$ undoes the exponential function with base $a$.