Algebra Examples

$\log_{2} (\frac{8}{{(x y)}^{2}})$

Step 1

Rewrite $\log_{2} (\frac{8}{{(x y)}^{2}})$ as $\log_{2} (8) - \log_{2} ({(x y)}^{2})$ .

$\log_{2} (8) - \log_{2} ({(x y)}^{2})$

Step 2

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

$\log_{2} (8) - (2 \log_{2} (x y))$

Step 3

Logarithm base $2$ of $8$ is $3$ .

$3 - (2 \log_{2} (x y))$

Step 4

Multiply $2$ by $- 1$ .

$3 - 2 \log_{2} (x y)$

Step 5

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

$3 - 2 (\log_{2} (x) + \log_{2} (y))$

Step 6

Apply the distributive property.

$3 - 2 \log_{2} (x) - 2 \log_{2} (y)$