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

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

Step 1

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

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

Step 2

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

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

Step 3

Multiply $4$ by $- 1$ .

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

Step 4

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

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

Step 5

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

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

Step 6

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

$\ln (2) + 2 \ln (x) + \ln (y) - 4 \ln (z)$