Chapter 8.5, Problem 3CYP

To determine

To find: The value of logarithmic expression ${\log }_{3}49$ .

Answer to Problem 3CYP

The value of expression ${\log }_{3}49$ is $3.5424$ .

Explanation of Solution

Given:

The logarithmic expression is ${\log }_{3}49$ .

Calculation:

Rewrite the logarithmic expression ${\log }_{3}49$ as ${\log }_{3}49={\log }_3{7}^2$ .

Use the Power Property of the logarithms to solve the equation ${\log }_{3}49={\log }_3{7}^2$ .

  $\begin{array}{c}{\log }_{3}49={\log }_3{7}^2\\ =2{\log }_{3}7\\ \approx 2\left(1.7712\right)\\ \approx 3.5424\end{array}$

Therefore, the value of expression ${\log }_{3}49$ is $3.5424$ .