View Single Post
 2010-07-08, 16:55 #1 Unregistered   2·3·7·132 Posts Exponentiation w/ independent variable Hello, I have a quick question regarding solving a weird log. Given the following: log (with base x-1) of x = f(x). Is it permissible to exponentiate in the following manner: (x-1)^y = (x-1)^(log base (x-1) of x) = (x-1)^y = x and then take the derivative y ln (x-1) = ln x 1/x-1 * y + y' * ln (x-1) = 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 x-1 = 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.