Q 87. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation.

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

Step-by-Step Solution

Answer

The solution to the equation, ${\log }_3 \left(x\right)=2$is, $x=9$.

Step 1. Given Information

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

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 ${\log }_3 \left(x\right)=2$.

Use rule of change from logarithm to exponents:

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

The solution to the given equation is, $x=9$.