Answer
(a). $x=-\dfrac{\log 18}{\log (8/3)}$
(b). $x=-2.946865$
Work Step by Step
$2^{3x+1}=3^{x-2},$
(a).
$\log (2^{3x+1})=\log (3^{x-2}),$
$(3x+1)\log 2=(x-2)\log 3,$
$\frac{3x+1}{x-2}=\frac{\log 3}{\log 2},$
$3x+1=(x-2)(\frac{\log 3}{\log 2}),$
$3x-x(\frac{\log 3}{\log 2})= -2(\frac{\log 3}{\log 2})-1,$
$x(3-\frac{\log 3}{\log 2})=-2(\frac{\log 3}{\log 2})-1,$
$$x=\frac{-2\left(\frac{\log 3}{\log 2}\right)-1}{3-\left(\frac{\log 3}{\log 2}\right)}=-\dfrac{-2\log 3-\log 2}{3\log 2-\log 3}=-\dfrac{\log 18}{\log (8/3)}$$
(b).
$x=-2.946865$
