Question

Solve the equation.

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

Short answer

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

Step-by-step solution

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 equationis,$x=9$.