Expand the Logarithmic Expression natural log of 12/5

$\ln (\frac{12}{5})$

Step 1

Rewrite $\ln (\frac{12}{5})$ as $\ln (12) - \ln (5)$ .

$\ln (12) - \ln (5)$

Step 2

Simplify each term.

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

$\ln (2^{2} \cdot 3) - \ln (5)$

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

$\ln (2^{2}) + \ln (3) - \ln (5)$

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

$2 \ln (2) + \ln (3) - \ln (5)$