Answer
The solution set is $\left\{-2\sqrt{2}, 2\sqrt{2}\right\}$.
Work Step by Step
RECALL:
$\log_a{x}=y \longrightarrow a^y=x, a\gt0, a\ne1$
Use the rule above to obtain:
$\log_3{(x^2+1)}=2
\\\longrightarrow 3^2=x^2+1
\\9=x^2+1$
Subtract by 1 on both sides of the equation to obtain:
$9-1=x^2+1-1
\\8=x^2$
Take the square root of both sides to obtain:
$\pm \sqrt{8} = x
\\\pm\sqrt{4(2)}=x
\\\pm \sqrt{2^2(2)} = x$
Simplify the radical to obtain:
$\pm2\sqrt{2}=x$
Thus, the solution set is $\left\{-2\sqrt{2}, 2\sqrt{2}\right\}$.
