Precalculus Examples

$2 \log_{2} (\frac{x^{4}}{w^{5}})$

Step 1

Rewrite $\log_{2} (\frac{x^{4}}{w^{5}})$ as $\log_{2} (x^{4}) - \log_{2} (w^{5})$ .

$2 (\log_{2} (x^{4}) - \log_{2} (w^{5}))$

Step 2

Expand $\log_{2} (x^{4})$ by moving $4$ outside the logarithm.

$2 (4 \log_{2} (x) - \log_{2} (w^{5}))$

Step 3

Expand $\log_{2} (w^{5})$ by moving $5$ outside the logarithm.

$2 (4 \log_{2} (x) - (5 \log_{2} (w)))$

Step 4

Multiply $5$ by $- 1$ .

$2 (4 \log_{2} (x) - 5 \log_{2} (w))$

Step 5

Apply the distributive property.

$2 (4 \log_{2} (x)) + 2 (- 5 \log_{2} (w))$

Step 6

Multiply $4$ by $2$ .

$8 \log_{2} (x) + 2 (- 5 \log_{2} (w))$

Step 7

Multiply $- 5$ by $2$ .

$8 \log_{2} (x) - 10 \log_{2} (w)$