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Old 2010-07-08, 16:55   #1

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Default Exponentiation w/ independent variable


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,

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