Chapter 6.5, Problem 39E

To determine

Tocalculate:The expression ${\log }_6\frac{3}{16}$ using change of base formula of logarithm.

Answer to Problem 39E

The required form of the expression is $\frac{\log \frac{3}{16}}{\log 6}$ .

Explanation of Solution

Given information:

The given expression is ${\log }_6\frac{3}{16}$ .

Formula used:

Change of base formula of logarithm:

  ${\log }_{n}m=\frac{\log m}{\log n}$

Consider the given expression ${\log }_6\frac{3}{16}$ .

Evaluate the expression using change of base formula of logarithm. ${\log }_{n}m=\frac{\log m}{\log n}$ .

  ${\log }_6\frac{3}{16}=\frac{\log \frac{3}{16}}{\log 6}$

Hence, therequired form of the expression is $\frac{\log \frac{3}{16}}{\log 6}$ .