Example Question - logarithm base 4
Here are examples of questions we've helped users solve.
Finding Inverse of Exponential Function
To find the inverse of the exponential function \( y = 4^x \), you need to solve for x in terms of y. Starting with the original function: \[ y = 4^x \] Swap the roles of x and y to begin finding the inverse function: \[ x = 4^y \] Now, solve for y by taking the logarithm with base 4 of both sides (since 4 is the base of the exponential function): \[ \log_4(x) = \log_4(4^y) \] By the properties of logarithms, \( \log_b(b^a) = a \), so: \[ \log_4(x) = y \] Therefore, the inverse function is: \[ y = \log_4(x) \] Looking at the options provided: A. \( y = x^{-4} \) - Incorrect, because this represents a power function, not a logarithmic function. B. \( y = (\frac{1}{4})^x \) - Incorrect, this is another exponential function, not the inverse of \( 4^x \). C. \( y = \log_4(x) \) - Correct, as proved above. D. \( y = - \log_4(x) \) - Incorrect, this is the negative of the logarithmic function. The correct answer is C: \( y = \log_4(x) \).
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)
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com