Precalculus Examples

$\log (\frac{5}{441})$

Step 1

Rewrite $\log (\frac{5}{441})$ as $\log (5) - \log (441)$ .

$\log (5) - \log (441)$

Step 2

Rewrite $\log (441)$ as $\log (3^{2} \cdot 7^{2})$ .

$\log (5) - \log (3^{2} \cdot 7^{2})$

Step 3

Rewrite $\log (3^{2} \cdot 7^{2})$ as $\log (3^{2}) + \log (7^{2})$ .

$\log (5) - (\log (3^{2}) + \log (7^{2}))$

Step 4

Simplify each term.

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Step 4.1

Expand $\log (3^{2})$ by moving $2$ outside the logarithm.

$\log (5) - (2 \log (3) + \log (7^{2}))$

Step 4.2

Expand $\log (7^{2})$ by moving $2$ outside the logarithm.

$\log (5) - (2 \log (3) + 2 \log (7))$

Step 5

Apply the distributive property.

$\log (5) - (2 \log (3)) - (2 \log (7))$

Step 6

Multiply $2$ by $- 1$ .

$\log (5) - 2 \log (3) - (2 \log (7))$

Step 7

Multiply $2$ by $- 1$ .

$\log (5) - 2 \log (3) - 2 \log (7)$