Chapter 4 - Exponential and Logarithmic Functions - Section 4.4 Logarithmic Functions - 4.4 Assess Your Understanding - Page 322: 103

$2\sqrt{2},-2\sqrt{2}$

$\because y=\log_a x \text{ is equivalent to } x= a^y$ $\therefore 2 = \log_3 {x^2+1} \text{ is equivalent to } x^2+1=3^2$ Solve the equation above to obtain: \begin{align*} x^2+1&=3^2\\\\ x^2+1&=9\\\\ x^2&=8\\\\ x&= \pm \sqrt{8}\\\\ x&=\pm\sqrt{4(2)}\\\\ x&=\pm2\sqrt2\\\\ x&=2\sqrt{2},-2\sqrt{2}\end{align*}