Question - Finding the Inverse of an Exponential Function
mathlogarithm base 4finding inverse exponential function4^x inverse functionsolving inverse exponential
Solution:
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^xTo find the inverse, switch x and y: x = 4^yNow 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)
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