Precalculus Examples

$\log_{3} (12 x^{7})$

Step 1

Rewrite $\log_{3} (12 x^{7})$ as $\log_{3} (12) + \log_{3} (x^{7})$ .

$\log_{3} (12) + \log_{3} (x^{7})$

Step 2

Expand $\log_{3} (x^{7})$ by moving $7$ outside the logarithm.

$\log_{3} (12) + 7 \log_{3} (x)$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Rewrite $\log_{3} (12)$ as $\log_{3} (2^{2} \cdot 3)$ .

$\log_{3} (2^{2} \cdot 3) + 7 \log_{3} (x)$

Step 3.2

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

$\log_{3} (2^{2}) + \log_{3} (3) + 7 \log_{3} (x)$

Step 3.3

Simplify each term.

Tap for more steps...

Step 3.3.1

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

$2 \log_{3} (2) + \log_{3} (3) + 7 \log_{3} (x)$

Step 3.3.2

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

$2 \log_{3} (2) + 1 + 7 \log_{3} (x)$