Question

In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible.

${\log }_{3}36-{\log }_{3}4$

Short answer

On simplifying the expression we get:

$2$

Step-by-step solution

Step 1. Given information

The given expression is ${\log }_{3}36-{\log }_{3}4$.

We have to condense the expression using logarithm properties.

Step 2. Identify the logarithm property to be used for the expression 

Use quotient property of logarithm which states:

${\log }_{a}M-{\log }_{a}N={\log }_a\left(\frac{M}{N}\right)$

Step 3. Use quotient property of logarithm 

$$\begin{gathered} {\log }_{3}36-{\log }_{3}4 \\ ={\log }_3\frac{36}{4} \\ ={\log }_{3}9 \\ ={\log }_3{3}^2 \\ =2({\log }_a{a}^b=b) \end{gathered}$$