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

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

Step 1

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

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

Step 2

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

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

Step 3

Multiply $2$ by $- 1$ .

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

Step 4

Simplify each term.

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

$\ln (2^{2}) - 2 \ln (x)$

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

$2 \ln (2) - 2 \ln (x)$