## Precalculus (6th Edition) Blitzer

Solution set = $\{ -\sqrt{\frac{\ln 50}{\ln 5}},\ \sqrt{\frac{\ln 50}{\ln 5}} \}$
$5^{x^{2}}=50$ 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 = $\{ -\sqrt{\frac{\ln 50}{\ln 5}},\ \sqrt{\frac{\ln 50}{\ln 5}} \}$