Answer
$x=±\sqrt {\frac{\ln(45)}{\ln(3)}}$
Work Step by Step
Use the natural log on both sides to solve for $x$.
$3^{x^2}=45$
$\ln(3^{x^2})=\ln(45)$
$x^2\ln(3)=\ln(45)$
$x^2=\frac{\ln(45)}{\ln(3)}$
$x=±\sqrt {\frac{\ln(45)}{\ln(3)}}$