Proof of basic logarithm property

Hi everyone:) I'm new here and as almost every newbie have come here with a problem:

I have defined lnx as

Then i proved that the sequence cinverges and some basic properties: it is inverse function of e^x and sum and subtraction. However I'm having trouble prooving formally that

for any real a( for natural numbers the proof is trivial of course). I suppose there would some kind of transformations using limits but i can't do it. Any help will be appreciated.

Thanks;)

Re: Proof of basic logarithm property

check here for more information specially the part for Analytic properties....

Logarithm - Wikipedia, the free encyclopedia

Re: Proof of basic logarithm property

I took a look. However there is no formal proof of what i want:X Thanks anyway:)

Re: Proof of basic logarithm property

If you know that and is the inverse of , and if you can use Taylor series, then