Answer
(a) $x=\frac{1}{2}+\frac{1}{2}\frac{\log 5}{\log 3}$
(b) $x\approx 1.232487$
Work Step by Step
(a) We need to solve:
$3^{2x-1}=5$
We take the log of both sides and use log rules to simplify:
$\log 3^{2x-1}=\log 5$
$(2x-1)\log 3=\log 5$
$2x-1=\frac{\log 5}{\log 3}$
$2x=1+\frac{\log 5}{\log 3}$
$x=\frac{1}{2}(1+\frac{\log 5}{\log 3})$
$x=\frac{1}{2}+\frac{1}{2}\frac{\log 5}{\log 3}$
(b) We solve using a calculator:
$x\approx 1.232487$
