Precalculus Examples

$\log_{3} (9 x^{3} y^{3} z^{6})$

Step 1

Rewrite $\log_{3} (9 x^{3} y^{3} z^{6})$ as $\log_{3} (9 x^{3} y^{3}) + \log_{3} (z^{6})$ .

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

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

$\log_{3} (9) + 3 \log_{3} (x) + 3 \log_{3} (y) + 6 \log_{3} (z)$

Step 7

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

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