Chapter 6.5, Problem 9E

To determine

To calculate: The correct value that matches with the expression ${\log }_{3}6-{\log }_{3}2$ .

Answer to Problem 9E

The expression ${\log }_{3}6-{\log }_{3}2$ matches with the expression ${\log }_{3}3$ .

Explanation of Solution

Given information:

The given expression is ${\log }_{3}6-{\log }_{3}2$ .

Formula used:

Quotient property of logarithm:

  $\log \frac{a}{b}=\log a-\log b$

Calculation:

Consider the expression is ${\log }_{3}6-{\log }_{3}2$ .

Com the expression using quotient property of logarithm, ${\log }_{b}m-{\log }_{b}n={\log }_b\frac{m}{n}$ .

  $\begin{array}{c}{\log }_{3}6-{\log }_{3}2={\log }_3\frac{6}{2}\\ ={\log }_{3}3\end{array}$

Hence, the correct value that matches with the expression ${\log }_{3}6-{\log }_{3}2$ is ${\log }_{3}3$ .