Precalculus Examples

$\log_{2} (5) - \log_{2} (8) - \log_{2} (10)$

Step 1

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

$\log_{2} (\frac{5}{8}) - \log_{2} (10)$

Step 2

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

$\log_{2} (\frac{\frac{5}{8}}{10})$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\log_{2} (\frac{5}{8} \cdot \frac{1}{10})$

Step 4

Cancel the common factor of $5$ .

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Step 4.1

Factor $5$ out of $10$ .

$\log_{2} (\frac{5}{8} \cdot \frac{1}{5 (2)})$

Step 4.2

Cancel the common factor.

$\log_{2} (\frac{5}{8} \cdot \frac{1}{5 \cdot 2})$

Step 4.3

Rewrite the expression.

$\log_{2} (\frac{1}{8} \cdot \frac{1}{2})$

Step 5

Multiply $\frac{1}{8}$ by $\frac{1}{2}$ .

$\log_{2} (\frac{1}{8 \cdot 2})$

Step 6

Simplify the expression.

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Step 6.1

Multiply $8$ by $2$ .

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

Step 6.2

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

$- 4$