Precalculus Examples

$\log_{b} (\frac{1}{10}) + \log_{b} (30)$

Step 1

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

$\log_{b} (\frac{1}{10} \cdot 30)$

Step 2

Cancel the common factor of $10$ .

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Step 2.1

Factor $10$ out of $30$ .

$\log_{b} (\frac{1}{10} \cdot (10 (3)))$

Step 2.2

Cancel the common factor.

$\log_{b} (\frac{1}{10} \cdot (10 \cdot 3))$

Step 2.3

Rewrite the expression.

$\log_{b} (3)$