Precalculus Examples

$\log_{b} (\frac{5}{6})$

Step 1

Rewrite $\log_{b} (\frac{5}{6})$ as $\log_{b} (5) - \log_{b} (6)$ .

$\log_{b} (5) - \log_{b} (6)$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\log_{b} (6)$ as $\log_{b} (2 (3))$ .

$\log_{b} (5) - \log_{b} (2 (3))$

Step 2.2

Rewrite $\log_{b} (2 (3))$ as $\log_{b} (2) + \log_{b} (3)$ .

$\log_{b} (5) - (\log_{b} (2) + \log_{b} (3))$

Step 2.3

Apply the distributive property.

$\log_{b} (5) - \log_{b} (2) - \log_{b} (3)$