Chapter 7.6, Problem 89S

To determine

To find: the equivalent exponential equation for the given logarithmic equation.

Answer to Problem 89S

The exponential equation is $5^2\text{=}25.$

Explanation of Solution

Given:

  ${\text{log}}_5\left(25\right)=2.$

Concept used:

In exponential form using the definition of the logarithm. If $\text{x and b }$ are positive real numbers and $\text{b}$ does not equal to $\text{1}$ ,then:

  ${\text{log}}_{\text{b}}\left(\text{x}\right)\text{=y}$ which is equivalent to the ${\text{b}}^{\text{y}}\text{=x}$ .

Calculation:

Here the given equation:

  ${\text{log}}_5\left(25\right)=2.$

Rewrite in exponential form using the definition of the logarithm. If $\text{x and b }$ are positive real numbers and $\text{b}$ does not equal to $\text{1}$ ,then:

  ${\text{log}}_{\text{b}}\left(\text{x}\right)\text{=y}$ which is equivalent to the ${\text{b}}^{\text{y}}\text{=x}$ .

So, the given equation ${\text{log}}_5\left(25\right)=2.$ can be equivalent to:

  $5^2\text{=}25.$

The equation is satisfied.

Hence, exponential equation is $5^2\text{=}25.$