Precalculus Examples

$\log_{3} (6^{3} \cdot 9^{6})$

Step 1

Rewrite $\log_{3} (6^{3} \cdot 9^{6})$ as $\log_{3} (6^{3}) + \log_{3} (9^{6})$ .

$\log_{3} (6^{3}) + \log_{3} (9^{6})$

Step 2

Expand $\log_{3} (6^{3})$ by moving $3$ outside the logarithm.

$3 \log_{3} (6) + \log_{3} (9^{6})$

Step 3

Expand $\log_{3} (9^{6})$ by moving $6$ outside the logarithm.

$3 \log_{3} (6) + 6 \log_{3} (9)$

Step 4

Logarithm base $3$ of $9$ is $2$ .

$3 \log_{3} (6) + 6 \cdot 2$

Step 5

Rewrite $\log_{3} (6)$ as $\log_{3} (2 (3))$ .

$3 \log_{3} (2 (3)) + 6 \cdot 2$

Step 6

Rewrite $\log_{3} (2 (3))$ as $\log_{3} (2) + \log_{3} (3)$ .

$3 (\log_{3} (2) + \log_{3} (3)) + 6 \cdot 2$

Step 7

Logarithm base $3$ of $3$ is $1$ .

$3 (\log_{3} (2) + 1) + 6 \cdot 2$

Step 8

Apply the distributive property.

$3 \log_{3} (2) + 3 \cdot 1 + 6 \cdot 2$

Step 9

Multiply $3$ by $1$ .

$3 \log_{3} (2) + 3 + 6 \cdot 2$

Step 10

Multiply $6$ by $2$ .

$3 \log_{3} (2) + 3 + 12$

Step 11

Add $3$ and $12$ .

$3 \log_{3} (2) + 15$