Answer
Solution set = $\{ -\sqrt{\frac{\ln 50}{\ln 5}},\ \sqrt{\frac{\ln 50}{\ln 5}} \}$
Work Step by Step
$5^{x^{2}}=50$
The RHS is not a power of 3. Apply $\ln $(...)
$\ln 5^{x^{2}}=\ln 50 ... \quad $ apply power rule
$ x^{2}\ln 5=\ln 50$
$ x^{2}=\displaystyle \frac{\ln 50}{\ln 5}$
$ x=\pm\sqrt{\frac{\ln 50}{\ln 5}}$
Solution set = $\{ -\sqrt{\frac{\ln 50}{\ln 5}},\ \sqrt{\frac{\ln 50}{\ln 5}} \}$
