Solve for x if $5^{x^2} = 625$.

$5^{x^2} = 625$

$5^{x^2} = 5^4$

Hence,
$x^2 = 4$

$x = \pm 2$
 

Another Solution
$5^{x^2} = 625$

$\ln 5^{x^2} = \ln 625$

$x^2 \ln 5 = \ln 625$

$x^2 = \dfrac{\ln 625}{\ln 5}$

$x^2 = 4$

$x = \pm 2$
 

Another Solution
Input the equation to your calculator

Hit CALC. Assign to x the number in the choices. The number that results to 625 is the answer.