Chapter 8.5, Problem 4CYU

To determine

To find: The value of logarithmic expression ${\log }_4\frac{3}{4}$ .

Answer to Problem 4CYU

The value of expression ${\log }_4\frac{3}{4}$ is $-0.2075$ .

Explanation of Solution

Given:

The logarithmic expression is ${\log }_4\frac{3}{4}$ .

Calculation:

Use the Quotient Rule of the logarithms to solve the expression ${\log }_4\frac{3}{4}$ .

  $\begin{array}{c}{\log }_4\frac{3}{4}={\log }_{4}3-{\log }_{4}4\\ \approx 0.7925-1\\ \approx -0.2075\end{array}$

Therefore, the value of expression ${\log }_4\frac{3}{4}$ is $-0.2075$ .