Expand the Logarithmic Expression natural log of (3y)/(x^5)

$\ln (\frac{3 y}{x^{5}})$

Step 1

Rewrite $\ln (\frac{3 y}{x^{5}})$ as $\ln (3 y) - \ln (x^{5})$ .

$\ln (3 y) - \ln (x^{5})$

Step 2

Expand $\ln (x^{5})$ by moving $5$ outside the logarithm.

$\ln (3 y) - (5 \ln (x))$

Step 3

Multiply $5$ by $- 1$ .

$\ln (3 y) - 5 \ln (x)$

Step 4

Rewrite $\ln (3 y)$ as $\ln (3) + \ln (y)$ .

$\ln (3) + \ln (y) - 5 \ln (x)$