Algebra Examples

$\log_{2} (4) - \log_{2} (16)$

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{2} (\frac{4}{16})$

Step 2

Cancel the common factor of $4$ and $16$ .

Tap for more steps...

Step 2.1

Factor $4$ out of $4$ .

$\log_{2} (\frac{4 (1)}{16})$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $4$ out of $16$ .

$\log_{2} (\frac{4 \cdot 1}{4 \cdot 4})$

Step 2.2.2

Cancel the common factor.

$\log_{2} (\frac{4 \cdot 1}{4 \cdot 4})$

Step 2.2.3

Rewrite the expression.

$\log_{2} (\frac{1}{4})$

Step 3

Logarithm base $2$ of $\frac{1}{4}$ is $- 2$ .

$- 2$