Precalculus Examples

$\log (4) - \log (10) + \log (250)$

Step 1

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

$\log (\frac{4}{10}) + \log (250)$

Step 2

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

$\log (\frac{4}{10} \cdot 250)$

Step 3

Cancel the common factor of $10$ .

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Step 3.1

Factor $10$ out of $250$ .

$\log (\frac{4}{10} \cdot (10 (25)))$

Step 3.2

Cancel the common factor.

$\log (\frac{4}{10} \cdot (10 \cdot 25))$

Step 3.3

Rewrite the expression.

$\log (4 \cdot 25)$

Step 4

Simplify the expression.

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Step 4.1

Multiply $4$ by $25$ .

$\log (100)$

Step 4.2

Logarithm base $10$ of $100$ is $2$ .

$2$