Answer
$$ y = \ln \left( {\frac{x}{3}} \right)$$
Work Step by Step
$$\eqalign{
& 9{e^{2y}} = {x^2} \cr
& {\text{divide by 9}} \cr
& {e^{2y}} = \frac{{{x^2}}}{9} \cr
& {\text{take the natural logarithm on both sides}} \cr
& \ln {e^{2y}} = \ln \left( {\frac{{{x^2}}}{9}} \right) \cr
& 2y = \ln \left( {\frac{{{x^2}}}{9}} \right) \cr
& {\text{solve for }}y \cr
& y = \frac{1}{2}\ln \left( {\frac{{{x^2}}}{9}} \right) \cr
& y = \ln {\left( {\frac{{{x^2}}}{9}} \right)^{1/2}} \cr
& y = \ln \left( {\frac{x}{3}} \right) \cr} $$
