How to find the inverse of y = log(4)x^2
x = 2log4 y
log4 y = (x/2)
4^log4 y = 4^(x/2)
y = 4^.5x
So I have to simplify and then get the exponential?
4^.5x = (4^.5)^x = 2^x
This is easy to see, since log_4(x^2) = 2log_4(x) = log_2(x)
Thanks to both!
To find the inverse of the function y = log(4)x^2, we need to switch the roles of the x and y variables and solve for y. Here's the step-by-step process:
Step 1: Start with the equation y = log(4)x^2.
Step 2: Switch the x and y variables to get x = log(4)y^2.
Step 3: Rewrite the logarithmic equation in exponential form. In this case, since the base of the logarithm is 4, we have 4^x = y^2.
Step 4: Take the square root of both sides of the equation to isolate y. Remember to include both positive and negative square roots. We get ±√(4^x) = ±y.
Step 5: Simplify √(4^x) to get ±2^x = ±y.
So, the inverse of y = log(4)x^2 is given by ±2^x.