Answer
$x=\pm2.146$
Work Step by Step
Given Expression
$e^{x^2}=100$
Take natural log of both sides.
$\ln{e^{x^2}}=\ln100$
Use the definition of a natural log and Power Rule of logarithms.
$x^2=\ln100$
Solve for $x$.
$x=\pm\sqrt{\ln100}$
$x=\pm2.146$