Precalculus Examples

$\log_{3} (9^{2} \cdot 2^{4})$

Step 1

Rewrite $\log_{3} (9^{2} \cdot 2^{4})$ as $\log_{3} (9^{2}) + \log_{3} (2^{4})$ .

$\log_{3} (9^{2}) + \log_{3} (2^{4})$

Step 2

Expand $\log_{3} (9^{2})$ by moving $2$ outside the logarithm.

$2 \log_{3} (9) + \log_{3} (2^{4})$

Step 3

Expand $\log_{3} (2^{4})$ by moving $4$ outside the logarithm.

$2 \log_{3} (9) + 4 \log_{3} (2)$

Step 4

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

$2 \cdot 2 + 4 \log_{3} (2)$

Step 5

Multiply $2$ by $2$ .

$4 + 4 \log_{3} (2)$