Q 88. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation.
${\log }_5\left(x\right)=3$

Step-by-Step Solution

Answer

The solution to the equation, ${\log }_5\left(x\right)=3$ is, $x=125$.

Step 1. Given Information

The given equation to be solved is ${\log }_5\left(x\right)=3$.

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 ${\log }_5\left(x\right)=3$.

Use rule of change from logarithm to exponents:

$$\begin{gathered} {\log }_5\left(x\right)=3 \\ x=5^3 \\ x=125 \end{gathered}$$

The solution to the given equation is, $x=125$.