Exponentiation w/ independent variable
Hello,
I have a quick question regarding solving a weird log.
Given the following: log (with base x1) of x = f(x). Is it permissible to exponentiate in the following manner:
(x1)^y = (x1)^(log base (x1) of x) =
(x1)^y = x and then take the derivative
y ln (x1) = ln x
1/x1 * y + y' * ln (x1) = 1/x ... ect solving for y' is trivial.
I know the alternate (which IS correct) is to rewrite using change of base yielding
log x/ log x1 = y and then taking the derivative. However, does the first method also arrive at the correct answer, or is it not legal?
Any help is appreciated,
Thanks.
