Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Multiply $4$ by $- 1$ .

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

Step 4

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

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

Step 5

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

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