Precalculus Examples

$\log_{3} (\frac{7 \cdot 11}{5})$

Step 1

Rewrite $\log_{3} (\frac{7 \cdot 11}{5})$ as $\log_{3} (7 \cdot 11) - \log_{3} (5)$ .

$\log_{3} (7 \cdot 11) - \log_{3} (5)$

Step 2

Multiply $7$ by $11$ .

$\log_{3} (77) - \log_{3} (5)$

Step 3

Simplify each term.

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Step 3.1

Rewrite $\log_{3} (77)$ as $\log_{3} (7 (11))$ .

$\log_{3} (7 (11)) - \log_{3} (5)$

Step 3.2

Rewrite $\log_{3} (7 (11))$ as $\log_{3} (7) + \log_{3} (11)$ .

$\log_{3} (7) + \log_{3} (11) - \log_{3} (5)$