Solving equation with logs and variables

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.

(Nerd)

Re: Solving equation with logs and variables

Can you show how you came to your answer?

Re: Solving equation with logs and variables

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.

Re: Solving equation with logs and variables

I assume again ...

(you used a capital F)

you should know that the inverse of an exponential function is a log function, but here is the derivation anyway ...

so ...

Re: Solving equation with logs and variables

Re: Solving equation with logs and variables

Change of base rule. I am aware of it. I see how that applies here now. Thanks!