Expand the Logarithmic Expression natural log of 1/(2x^2)

$\ln (\frac{1}{2 x^{2}})$

Step 1

Rewrite $\ln (\frac{1}{2 x^{2}})$ as $\ln (1) - \ln (2 x^{2})$ .

$\ln (1) - \ln (2 x^{2})$

Step 2

The natural logarithm of $1$ is $0$ .

$0 - \ln (2 x^{2})$

Step 3

Subtract $\ln (2 x^{2})$ from $0$ .

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

Step 4

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

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

Step 5

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

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

Step 6

Apply the distributive property.

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

Step 7

Multiply $2$ by $- 1$ .

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