Q 103. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation. 

${\log }_3\left(x^2+1\right)=2$

Step-by-Step Solution

Answer

The solution to the equation, ${\log }_3\left(x^2+1\right)=2$is, $x=2\sqrt{2}$.

Step 1. Given Information

The given equation to be solved is ${\log }_3\left(x^2+1\right)=2$.

Step 2. Formula used

Rule of change from logarithm to exponents: 

${\log }_{a}b=y\Rightarrow a^y=b$

Step 3. Finding Solution

The given equation is ${\log }_3\left(x^2+1\right)=2$.

Use rule of change from logarithm to exponents: 

$$\begin{gathered} {\log }_3\left(x^2+1\right)=2 \\ {x}^2+1=3^2 \\ {x}^2+1=9 \\ {x}^2=8 \\ x=2\sqrt{2} \end{gathered}$$

The solution to the given equation is,  $x=2\sqrt{2}$.