Can you show how you came to your answer?
Problem: F(x) = 4^(x) for all real values of x. If p>1 and q>1, then f^(-1)(p)f^(-1)(q)=?
The notation above for f^(-1) means inverse function.
The answer is log(base 4) p x log(base 4)q
I first attempted to solve for the inverse function by switching y and x and then solving for y. This did not get me log (base4) x, which the book says is the inverse of the exponential function.
I didn't come to the right answer, but I have y=4^(x) I switched x and y to solve for the inverse. x=4^(y) I took the log of both sides logx= ylog4. Then I got logx/log4. I then plugged in p and q and fiddled with it from there to no avail.
Which logarithm did you use? gives a different function for every different a, so its inverse is a different function for every a. If you had used , Since , log_4(4)= 1 so your "log x/log 4" is just . For any other logarithm, it is true that . That's a property of logarithms worth knowing: