Answer
$$ y = \frac{{\ln 2}}{{\ln \left( {3/2} \right)}}$$
Work Step by Step
$$\eqalign{
& {3^y} = {2^{y + 1}} \cr
& {\text{take the natural logarithm on both sides}} \cr
& \ln {3^y} = \ln {2^{y + 1}} \cr
& {\text{use the power property}} \cr
& y\ln 3 = \left( {y + 1} \right)\ln 2 \cr
& y\ln 3 = y\ln 2 + \ln 2 \cr
& {\text{solve for }}y \cr
& y\ln 3 - y\ln 2 = \ln 2 \cr
& y\left( {\ln 3 - \ln 2} \right) = \ln 2 \cr
& y = \frac{{\ln 2}}{{\ln 3 - \ln 2}} \cr
& y = \frac{{\ln 2}}{{\ln \left( {3/2} \right)}} \cr} $$
