Precalculus Examples

$\log_{3} (9 x^{9} y^{4})$

Step 1

Rewrite $\log_{3} (9 x^{9} y^{4})$ as $\log_{3} (9 x^{9}) + \log_{3} (y^{4})$ .

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

Step 2

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

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

Step 3

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

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

Step 4

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

$\log_{3} (9) + 9 \log_{3} (x) + 4 \log_{3} (y)$

Step 5

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

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