Inverse of Exponential Function
The question asks for the inverse of the exponential function \( y = 4^x \).
To find the inverse function, we typically swap \( x \) and \( y \) and then solve for \( y \).
Starting with \( y = 4^x \), we swap \( x \) and \( y \) to get \( x = 4^y \).
Now we need to solve for \( y \). To do this, we take the logarithm base 4 of both sides:
\( \log_4(x) = \log_4(4^y) \).
Using the property of logarithms that \( \log_b(b^a) = a \), we simplify the right side to get:
\( \log_4(x) = y \).
So, the inverse function of \( y = 4^x \) is \( y = \log_4(x) \).
The correct answer is:
C. \( y = \log_4(x) \).
