Expand the Logarithmic Expression natural log of (4a)^3

$\ln ({(4 a)}^{3})$

Step 1

Expand $\ln ({(4 a)}^{3})$ by moving $3$ outside the logarithm.

$3 \ln (4 a)$

Step 2

Rewrite $\ln (4 a)$ as $\ln (4) + \ln (a)$ .

$3 (\ln (4) + \ln (a))$

Step 3

Simplify each term.

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

$3 (\ln (2^{2}) + \ln (a))$

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

$3 (2 \ln (2) + \ln (a))$

Step 4

Apply the distributive property.

$3 (2 \ln (2)) + 3 \ln (a)$

Step 5

Multiply $2$ by $3$ .

$6 \ln (2) + 3 \ln (a)$