Precalculus Examples

$\log_{2} ({(x^{6} \cdot y)}^{2})$

Step 1

Expand $\log_{2} ({(x^{6} \cdot y)}^{2})$ by moving $2$ outside the logarithm.

$2 \log_{2} (x^{6} \cdot y)$

Step 2

Rewrite $\log_{2} (x^{6} \cdot y)$ as $\log_{2} (x^{6}) + \log_{2} (y)$ .

$2 (\log_{2} (x^{6}) + \log_{2} (y))$

Step 3

Expand $\log_{2} (x^{6})$ by moving $6$ outside the logarithm.

$2 (6 \log_{2} (x) + \log_{2} (y))$

Step 4

Apply the distributive property.

$2 (6 \log_{2} (x)) + 2 \log_{2} (y)$

Step 5

Multiply $6$ by $2$ .

$12 \log_{2} (x) + 2 \log_{2} (y)$