Answer
The solution set is $ \left \{ \pm \sqrt {\frac{\ln (50)}{\ln(5)}} \approx \pm 1.56 \right \}$.
Work Step by Step
The given equation is
$5^{x^{2}}=50$
Take the natural logarithm on both sides.
$\ln (5^{x^{2}})=\ln (50)$
Use the power rule.
$x^2 \ln (5)=\ln (50)$
Divide both sides by $\ln(5)$.
$\frac{x^2 \ln (5)}{\ln(5)}=\frac{\ln (50)}{\ln(5)}$
Simplify.
$x^2=\frac{\ln (50)}{\ln(5)}$
Take the square root on both sides.
$\sqrt {x^2}=\pm \sqrt {\frac{\ln (50)}{\ln(5)}}$
$x=\pm \sqrt {\frac{\ln (50)}{\ln(5)}}$
$x=\pm 1.56$.
