Answer
Solution set = $\{ -\sqrt{\frac{\ln 45}{\ln 3}},\ \sqrt{\frac{\ln 45}{\ln 3}} \}$
Work Step by Step
$3^{x^{2}}=45$
The RHS is not a power of 3. Apply $\ln $(...)
$\ln 3^{x^{2}}=\ln 45 ... \quad $ apply power rule
$ x^{2}\ln 3=\ln 45$
$ x^{2}=\displaystyle \frac{\ln 45}{\ln 3}$
$ x=\pm\sqrt{\frac{\ln 45}{\ln 3}}$
Solution set = $\{ -\sqrt{\frac{\ln 45}{\ln 3}},\ \sqrt{\frac{\ln 45}{\ln 3}} \}$
