Precalculus Examples

$\log_{3} (\frac{x^{5} y^{7}}{8})$

Step 1

Rewrite $\log_{3} (\frac{x^{5} y^{7}}{8})$ as $\log_{3} (x^{5} y^{7}) - \log_{3} (8)$ .

$\log_{3} (x^{5} y^{7}) - \log_{3} (8)$

Step 2

Rewrite $\log_{3} (8)$ as $\log_{3} (2^{3})$ .

$\log_{3} (x^{5} y^{7}) - \log_{3} (2^{3})$

Step 3

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

$\log_{3} (x^{5} y^{7}) - (3 \log_{3} (2))$

Step 4

Multiply $3$ by $- 1$ .

$\log_{3} (x^{5} y^{7}) - 3 \log_{3} (2)$

Step 5

Rewrite $\log_{3} (x^{5} y^{7})$ as $\log_{3} (x^{5}) + \log_{3} (y^{7})$ .

$\log_{3} (x^{5}) + \log_{3} (y^{7}) - 3 \log_{3} (2)$

Step 6

Expand $\log_{3} (x^{5})$ by moving $5$ outside the logarithm.

$5 \log_{3} (x) + \log_{3} (y^{7}) - 3 \log_{3} (2)$

Step 7

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

$5 \log_{3} (x) + 7 \log_{3} (y) - 3 \log_{3} (2)$