Write as a Single Logarithm 3/5 natural log of x-7 natural log of y

$\frac{3}{5} \ln (x) - 7 \ln (y)$

Simplify each term.

Simplify $\frac{3}{5} \ln (x)$ by moving $\frac{3}{5}$ inside the logarithm.

$\ln (x^{\frac{3}{5}}) - 7 \ln (y)$

Simplify $- 7 \ln (y)$ by moving $7$ inside the logarithm.

$\ln (x^{\frac{3}{5}}) - \ln (y^{7})$

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\ln (\frac{x^{\frac{3}{5}}}{y^{7}})$