Precalculus Examples

$\log_{2} (10) - \log_{2} (35) + \log_{2} (28)$

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

$\log_{2} (\frac{10}{35}) + \log_{2} (28)$

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

$\log_{2} (\frac{10}{35} \cdot 28)$

Cancel the common factor of $7$ .

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Factor $7$ out of $35$ .

$\log_{2} (\frac{10}{7 (5)} \cdot 28)$

Factor $7$ out of $28$ .

$\log_{2} (\frac{10}{7 \cdot 5} \cdot (7 \cdot 4))$

Cancel the common factor.

$\log_{2} (\frac{10}{7 \cdot 5} \cdot (7 \cdot 4))$

Rewrite the expression.

$\log_{2} (\frac{10}{5} \cdot 4)$

Combine $\frac{10}{5}$ and $4$ .

$\log_{2} (\frac{10 \cdot 4}{5})$

Simplify the expression.

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Multiply $10$ by $4$ .

$\log_{2} (\frac{40}{5})$

Logarithm base $2$ of $\frac{40}{5}$ is $3$ .

$3$