Questions: Find the inverse of (x=e^y).

Solution Steps

To find the inverse of the function \( x = e^y \), we need to express \( y \) in terms of \( x \). This involves taking the natural logarithm of both sides of the equation to solve for \( y \).

Given the equation \( x = e^y \), we want to find the inverse function by expressing \( y \) in terms of \( x \). To do this, we take the natural logarithm of both sides:

\[ \ln(x) = \ln(e^y) \]

Using the property of logarithms that \( \ln(e^y) = y \), we simplify the equation:

\[ y = \ln(x) \]

Final Answer