Precalculus Examples

$\log (5^{3} \cdot 12^{6})$

Step 1

Rewrite $\log (5^{3} \cdot 12^{6})$ as $\log (5^{3}) + \log (12^{6})$ .

$\log (5^{3}) + \log (12^{6})$

Step 2

Expand $\log (5^{3})$ by moving $3$ outside the logarithm.

$3 \log (5) + \log (12^{6})$

Step 3

Expand $\log (12^{6})$ by moving $6$ outside the logarithm.

$3 \log (5) + 6 \log (12)$

Step 4

Rewrite $\log (12)$ as $\log (2^{2} \cdot 3)$ .

$3 \log (5) + 6 \log (2^{2} \cdot 3)$

Step 5

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

$3 \log (5) + 6 (\log (2^{2}) + \log (3))$

Step 6

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

$3 \log (5) + 6 (2 \log (2) + \log (3))$

Step 7

Apply the distributive property.

$3 \log (5) + 6 (2 \log (2)) + 6 \log (3)$

Step 8

Multiply $2$ by $6$ .

$3 \log (5) + 12 \log (2) + 6 \log (3)$