exponent equation

**fran1942** · March 28th 2011, 01:41 PM

Hello, I have the following equation:

5^x = 4^x+1

I am confident the first two steps are:
(using common log)

a) log5^x = log 4^x+1
b) xlog5 = x+1log 4

However I can not figure out to finish the problem.

Can someone please help ?
Thanks kindly

**e^(i*pi)** · March 28th 2011, 01:45 PM

$5^x = 4^{x+1}$ . It's a very important bracket there, as you wrote it +1 is not in the exponent. Also $(x+1)\log(4) \neq x+1\log(4)$

Nonetheless you're on the right track: $x\log_{10}(5) = x\log_{10}(4) + \log_{10}(4) \implies x\log_{10}(5) - x\log_{10}(4) = \log_{10}(4)$

x is now a factor of both terms on the LHS. Can you finish?

edit: if the answer has $\log_{10}(2)$ in then recall $\log(4) = 2\log(2)$

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