Precalculus Examples

$\log_{3} (\frac{x^{6} y^{7}}{7})$

Step 1

Rewrite $\log_{3} (\frac{x^{6} y^{7}}{7})$ as $\log_{3} (x^{6} y^{7}) - \log_{3} (7)$ .

$\log_{3} (x^{6} y^{7}) - \log_{3} (7)$

Step 2

Rewrite $\log_{3} (x^{6} y^{7})$ as $\log_{3} (x^{6}) + \log_{3} (y^{7})$ .

$\log_{3} (x^{6}) + \log_{3} (y^{7}) - \log_{3} (7)$

Step 3

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

$6 \log_{3} (x) + \log_{3} (y^{7}) - \log_{3} (7)$

Step 4

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

$6 \log_{3} (x) + 7 \log_{3} (y) - \log_{3} (7)$