Precalculus Examples

$\log_{3} (\frac{x^{4}}{y^{8}})$

Step 1

Rewrite $\log_{3} (\frac{x^{4}}{y^{8}})$ as $\log_{3} (x^{4}) - \log_{3} (y^{8})$ .

$\log_{3} (x^{4}) - \log_{3} (y^{8})$

Step 2

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

$4 \log_{3} (x) - \log_{3} (y^{8})$

Step 3

Expand $\log_{3} (y^{8})$ by moving $8$ outside the logarithm.

$4 \log_{3} (x) - (8 \log_{3} (y))$

Step 4

Multiply $8$ by $- 1$ .

$4 \log_{3} (x) - 8 \log_{3} (y)$