Precalculus Examples

$\log_{4} ({({(\frac{x \cdot y}{z})}^{5})}^{6})$

Step 1

Expand $\log_{4} ({({(\frac{x \cdot y}{z})}^{5})}^{6})$ by moving $6$ outside the logarithm.

$6 \log_{4} ({(\frac{x \cdot y}{z})}^{5})$

Step 2

Expand $\log_{4} ({(\frac{x \cdot y}{z})}^{5})$ by moving $5$ outside the logarithm.

$6 (5 \log_{4} (\frac{x \cdot y}{z}))$

Step 3

Multiply $5$ by $6$ .

$30 \log_{4} (\frac{x \cdot y}{z})$

Step 4

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

$30 (\log_{4} (x \cdot y) - \log_{4} (z))$

Step 5

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

$30 (\log_{4} (x) + \log_{4} (y) - \log_{4} (z))$

Step 6

Apply the distributive property.

$30 \log_{4} (x) + 30 \log_{4} (y) + 30 (- \log_{4} (z))$

Step 7

Multiply $- 1$ by $30$ .

$30 \log_{4} (x) + 30 \log_{4} (y) - 30 \log_{4} (z)$