Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Multiply $2$ by $- 1$ .

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

Step 4

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

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

Step 5

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

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

Step 6

Logarithm base $2$ of $2$ is $1$ .

$1 + \log_{2} (x) + \log_{2} (z) - 2 \log_{2} (y)$