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

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

Step 1

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

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

Step 2

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

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

Step 3

Multiply $4$ by $- 1$ .

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

Step 4

Rewrite $\ln (2 x)$ as $\ln (2) + \ln (x)$ .

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