Precalculus Examples

$\log_{3} (\frac{x y^{4}}{z^{5}})$

Step 1

Rewrite $\log_{3} (\frac{x y^{4}}{z^{5}})$ as $\log_{3} (x y^{4}) - \log_{3} (z^{5})$ .

$\log_{3} (x y^{4}) - \log_{3} (z^{5})$

Step 2

Expand $\log_{3} (z^{5})$ by moving $5$ outside the logarithm.

$\log_{3} (x y^{4}) - (5 \log_{3} (z))$

Step 3

Multiply $5$ by $- 1$ .

$\log_{3} (x y^{4}) - 5 \log_{3} (z)$

Step 4

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

$\log_{3} (x) + \log_{3} (y^{4}) - 5 \log_{3} (z)$

Step 5

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

$\log_{3} (x) + 4 \log_{3} (y) - 5 \log_{3} (z)$