Q 96. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation.

 ${\log }_{5}625=x$

Step-by-Step Solution

Answer

The solution to the equation, ${\log }_{5}625=x$ is, $x=4$.

Step 1. Given Information

The given equation to be solved is ${\log }_{5}625=x$.

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 ${\log }_{5}625=x$.

Use rule of change from logarithm to exponents: 

$$\begin{gathered} {\log }_{5}625=x \\ {5}^x=625 \\ (5{)}^x=(5{)}^4 \\ x=4 \end{gathered}$$

The solution to the given equation is, $x=4$.