Precalculus Examples

$\log_{3} ({(27 x)}^{2})$

Step 1

Expand $\log_{3} ({(27 x)}^{2})$ by moving $2$ outside the logarithm.

$2 \log_{3} (27 x)$

Step 2

Rewrite $\log_{3} (27 x)$ as $\log_{3} (27) + \log_{3} (x)$ .

$2 (\log_{3} (27) + \log_{3} (x))$

Step 3

Logarithm base $3$ of $27$ is $3$ .

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $2$ by $3$ .

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