Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Multiply $3$ by $- 1$ .

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

Step 5

Apply the distributive property.

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

Step 6

Multiply $- 3$ by $6$ .

$6 \log_{3} (x) - 18 \log_{3} (y)$