Precalculus Examples

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

Step 1

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

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

Step 2

Rewrite $\log_{3} (\frac{x^{4}}{y})$ as $\log_{3} (x^{4}) - \log_{3} (y)$ .

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

Step 3

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

$3 (4 \log_{3} (x) - \log_{3} (y))$

Step 4

Apply the distributive property.

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

Step 5

Multiply $4$ by $3$ .

$12 \log_{3} (x) + 3 (- \log_{3} (y))$

Step 6

Multiply $- 1$ by $3$ .

$12 \log_{3} (x) - 3 \log_{3} (y)$