Trigonometry Examples

$\log (312)$

Step 1

Rewrite $\log (312)$ as $\log (2^{3} \cdot 3 \cdot 13)$ .

$\log (2^{3} \cdot 3 \cdot 13)$

Step 2

Rewrite $\log (2^{3} \cdot 3 \cdot 13)$ as $\log (2^{3} \cdot 3) + \log (13)$ .

$\log (2^{3} \cdot 3) + \log (13)$

Step 3

Simplify each term.

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Step 3.1

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

$\log (2^{3}) + \log (3) + \log (13)$

Step 3.2

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

$3 \log (2) + \log (3) + \log (13)$