Precalculus Examples

$\log_{4} ({(\frac{256}{a})}^{3})$

Step 1

Expand $\log_{4} ({(\frac{256}{a})}^{3})$ by moving $3$ outside the logarithm.

$3 \log_{4} (\frac{256}{a})$

Step 2

Rewrite $\log_{4} (\frac{256}{a})$ as $\log_{4} (256) - \log_{4} (a)$ .

$3 (\log_{4} (256) - \log_{4} (a))$

Step 3

Logarithm base $4$ of $256$ is $4$ .

$3 (4 - \log_{4} (a))$

Step 4

Apply the distributive property.

$3 \cdot 4 + 3 (- \log_{4} (a))$

Step 5

Multiply $3$ by $4$ .

$12 + 3 (- \log_{4} (a))$

Step 6

Multiply $- 1$ by $3$ .

$12 - 3 \log_{4} (a)$