Chapter 8.5, Problem 7CYU

To determine

To find: The value of logarithmic expression ${\log }_{5}49$ .

Answer to Problem 7CYU

The value of expression ${\log }_{5}49$ is $2.4182$ .

Explanation of Solution

Given:

The logarithmic expression is ${\log }_{5}49$ .

Calculation:

Rewrite the logarithmic expression ${\log }_{5}49$ as ${\log }_{5}49={\log }_5{7}^2$ .

Use the Power Rule of logarithms to solve the equation ${\log }_{5}49={\log }_5{7}^2$ .

  $\begin{array}{c}{\log }_{5}49={\log }_5{7}^2\\ =2{\log }_{5}7\\ \approx 2\left(1.2091\right)\\ \approx 2.4182\end{array}$

Therefore, the value of expression ${\log }_{5}49$ is $2.4182$ .