Chapter 8.5, Problem 14PPS

To determine

To find: The value of logarithmic expression ${\log }_4\frac{2}{3}$ .

Answer to Problem 14PPS

The value of expression ${\log }_4\frac{2}{3}$ is $-0.2925$ .

Explanation of Solution

Given:

The logarithmic expression is ${\log }_4\frac{2}{3}$ .

Calculation:

Use the Quotient Property of the logarithms to solve the expression ${\log }_4\frac{2}{3}$ .

  $\begin{array}{c}{\log }_4\frac{2}{3}={\log }_{4}2-{\log }_{4}3\\ \approx 0.5-0.7925\\ \approx -0.2925\end{array}$

Therefore, the value of expression ${\log }_4\frac{2}{3}$ is $-0.2925$ .