Finding the Inverse of an Exponential Function
The question asks for the inverse of the exponential function y = 4^x. To find the inverse function, we typically interchange the roles of x and y and then solve for y. Here's how this is done for the given function:
Original function: y = 4^x
To find the inverse, switch x and y: x = 4^y
Now to solve for y, we can take the logarithm base 4 of both sides, which gives us the inverse function:
y = log_4(x)
This is because the logarithm base 4 of 4 raised to some power will give us that power, in this case, y.
Therefore, the correct answer is:
C. y = log_4(x)
