Precalculus Examples

$\log_{3} ({(9 x)}^{3})$

Step 1

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

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

Step 2

Rewrite $\log_{3} (9 x)$ as $\log_{3} (9) + \log_{3} (x)$ .

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

Step 3

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

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $3$ by $2$ .

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