Precalculus Examples

$\log_{2} (\frac{x y^{2}}{64})$

Step 1

Rewrite $\log_{2} (\frac{x y^{2}}{64})$ as $\log_{2} (x y^{2}) - \log_{2} (64)$ .

$\log_{2} (x y^{2}) - \log_{2} (64)$

Step 2

Logarithm base $2$ of $64$ is $6$ .

$\log_{2} (x y^{2}) - 1 \cdot 6$

Step 3

Multiply $- 1$ by $6$ .

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

Step 4

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

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

Step 5

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

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