Expand the Logarithmic Expression natural log of (3e^4)/(x^2)

$\ln (\frac{3 e^{4}}{x^{2}})$

Step 1

Rewrite $\ln (\frac{3 e^{4}}{x^{2}})$ as $\ln (3 e^{4}) - \ln (x^{2})$ .

$\ln (3 e^{4}) - \ln (x^{2})$

Step 2

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

$\ln (3 e^{4}) - (2 \ln (x))$

Step 3

Multiply $2$ by $- 1$ .

$\ln (3 e^{4}) - 2 \ln (x)$

Step 4

Rewrite $\ln (3 e^{4})$ as $\ln (3) + \ln (e^{4})$ .

$\ln (3) + \ln (e^{4}) - 2 \ln (x)$

Step 5

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

$\ln (3) + 4 \ln (e) - 2 \ln (x)$

Step 6

The natural logarithm of $e$ is $1$ .

$\ln (3) + 4 \cdot 1 - 2 \ln (x)$

Step 7

Multiply $4$ by $1$ .

$\ln (3) + 4 - 2 \ln (x)$