Precalculus Examples

$6 \log (8) \cdot 11 + 12 \log (8) \cdot 2$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\log (8)$ as $\log (2^{3})$ .

$6 \log (2^{3}) \cdot 11 + 12 \log (8) \cdot 2$

Step 1.2

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

$6 (3 \log (2)) \cdot 11 + 12 \log (8) \cdot 2$

Step 1.3

Multiply $3$ by $6$ .

$18 \log (2) \cdot 11 + 12 \log (8) \cdot 2$

Step 1.4

Multiply $11$ by $18$ .

$198 \log (2) + 12 \log (8) \cdot 2$

Step 1.5

Rewrite $\log (8)$ as $\log (2^{3})$ .

$198 \log (2) + 12 \log (2^{3}) \cdot 2$

Step 1.6

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

$198 \log (2) + 12 (3 \log (2)) \cdot 2$

Step 1.7

Multiply $3$ by $12$ .

$198 \log (2) + 36 \log (2) \cdot 2$

Step 1.8

Multiply $2$ by $36$ .

$198 \log (2) + 72 \log (2)$

Step 2

Add $198 \log (2)$ and $72 \log (2)$ .

$270 \log (2)$