Evaluate log base 3 of 9+ log base 3 of 36- log base 3 of 4

$\log_{3} (9) + \log_{3} (36) - \log_{3} (4)$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{3} (9 \cdot 36) - \log_{3} (4)$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{3} (\frac{9 \cdot 36}{4})$

Step 3

Cancel the common factor of $36$ and $4$ .

Factor $4$ out of $9 \cdot 36$ .

$\log_{3} (\frac{4 (9 \cdot 9)}{4})$

Cancel the common factors.

Factor $4$ out of $4$ .

$\log_{3} (\frac{4 (9 \cdot 9)}{4 (1)})$

Cancel the common factor.

$\log_{3} (\frac{4 (9 \cdot 9)}{4 \cdot 1})$

Rewrite the expression.

$\log_{3} (\frac{9 \cdot 9}{1})$

Divide $9 \cdot 9$ by $1$ .

$\log_{3} (9 \cdot 9)$

Step 4

Simplify the expression.

Multiply $9$ by $9$ .

$\log_{3} (81)$

Logarithm base $3$ of $81$ is $4$ .

$4$