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
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
$\displaystyle 5^x = 4^{x+1}$. It's a very important bracket there, as you wrote it +1 is not in the exponent. Also $\displaystyle (x+1)\log(4) \neq x+1\log(4)$
Nonetheless you're on the right track: $\displaystyle x\log_{10}(5) = x\log_{10}(4) + \log_{10}(4) \implies x\log_{10}(5) - x\log_{10}(4) = \log_{10}(4)$
x is now a factor of both terms on the LHS. Can you finish?
edit: if the answer has $\displaystyle \log_{10}(2)$ in then recall $\displaystyle \log(4) = 2\log(2)$