Answer
(a) $x=\frac{\log 4}{\log\frac{5}{4}}$
(b) $x\approx 6.212567$
Work Step by Step
(a) We need to solve:
$5^{x}=4^{x+1}$
We take the log of both sides and use log rules to simplify:
$\log 5^{x}=\log 4^{x+1}$
$x \log5 =(x+1) \log4$
$x \log5 =x\log 4+\log 4$
$x\log 5-x \log4 =\log 4$
$x(\log 5-\log 4)=\log 4$
$x=\frac{\log 4}{\log\frac{5}{4}}$
(b) We solve using a calculator:
$x\approx 6.212567$
