# Math Help - exponent equation

1. ## exponent equation

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.

Thanks kindly

2. $5^x = 4^{x+1}$. 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 $\log(4) = 2\log(2)$