Precalculus Examples

$\log_{2} (\frac{2}{3}) + \log_{2} (\frac{3}{32})$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{2} (\frac{2}{3} \cdot \frac{3}{32})$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $32$ .

$\log_{2} (\frac{2}{3} \cdot \frac{3}{2 (16)})$

Step 2.2

Cancel the common factor.

$\log_{2} (\frac{2}{3} \cdot \frac{3}{2 \cdot 16})$

Step 2.3

Rewrite the expression.

$\log_{2} (\frac{1}{3} \cdot \frac{3}{16})$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

$\log_{2} (\frac{1}{3} \cdot \frac{3}{16})$

Step 3.2

Rewrite the expression.

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

Step 4

Logarithm base $2$ of $\frac{1}{16}$ is $- 4$ .

$- 4$