Simplify/Condense 3 natural log of x-1/3* natural log of y

$3 \ln (x) - \frac{1}{3} \cdot \ln (y)$

Simplify each term.

Simplify $3 \ln (x)$ by moving $3$ inside the logarithm.

$\ln (x^{3}) - \frac{1}{3} \cdot \ln (y)$

Multiply $- \frac{1}{3} \ln (y)$ .

Reorder $\ln (y)$ and $\frac{1}{3}$ .

$\ln (x^{3}) - (\frac{1}{3} \ln (y))$

Simplify $\frac{1}{3} \ln (y)$ by moving $\frac{1}{3}$ inside the logarithm.

$\ln (x^{3}) - \ln (y^{\frac{1}{3}})$

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

$\ln (\frac{x^{3}}{y^{\frac{1}{3}}})$