Precalculus Examples

$\log (\frac{4}{27})$

Step 1

Rewrite $\log (\frac{4}{27})$ as $\log (4) - \log (27)$ .

$\log (4) - \log (27)$

Step 2

Rewrite $\log (27)$ as $\log (3^{3})$ .

$\log (4) - \log (3^{3})$

Step 3

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

$\log (4) - (3 \log (3))$

Step 4

Multiply $3$ by $- 1$ .

$\log (4) - 3 \log (3)$

Step 5

Simplify each term.

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Step 5.1

Rewrite $\log (4)$ as $\log (2^{2})$ .

$\log (2^{2}) - 3 \log (3)$

Step 5.2

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

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