Precalculus Examples

$\log ({(a^{4} \cdot b)}^{6})$

Step 1

Expand $\log ({(a^{4} \cdot b)}^{6})$ by moving $6$ outside the logarithm.

$6 \log (a^{4} \cdot b)$

Step 2

Rewrite $\log (a^{4} \cdot b)$ as $\log (a^{4}) + \log (b)$ .

$6 (\log (a^{4}) + \log (b))$

Step 3

Expand $\log (a^{4})$ by moving $4$ outside the logarithm.

$6 (4 \log (a) + \log (b))$

Step 4

Apply the distributive property.

$6 (4 \log (a)) + 6 \log (b)$

Step 5

Multiply $4$ by $6$ .

$24 \log (a) + 6 \log (b)$