Precalculus Examples

$\log (\frac{6}{11}) \cdot 5$

Step 1

Rewrite $\log (\frac{6}{11})$ as $\log (6) - \log (11)$ .

$(\log (6) - \log (11)) \cdot 5$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\log (6)$ as $\log (2 (3))$ .

$(\log (2 (3)) - \log (11)) \cdot 5$

Step 2.2

Rewrite $\log (2 (3))$ as $\log (2) + \log (3)$ .

$(\log (2) + \log (3) - \log (11)) \cdot 5$

Step 3

Apply the distributive property.

$\log (2) \cdot 5 + \log (3) \cdot 5 - \log (11) \cdot 5$

Step 4

Simplify.

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Step 4.1

Move $5$ to the left of $\log (2)$ .

$5 \cdot \log (2) + \log (3) \cdot 5 - \log (11) \cdot 5$

Step 4.2

Move $5$ to the left of $\log (3)$ .

$5 \cdot \log (2) + 5 \cdot \log (3) - \log (11) \cdot 5$

Step 4.3

Multiply $5$ by $- 1$ .

$5 \cdot \log (2) + 5 \cdot \log (3) - 5 \log (11)$

Step 5

Multiply $5$ by $\log (3)$ .

$5 \log (2) + 5 \log (3) - 5 \log (11)$