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

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

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

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

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

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

Reorder factors in $\ln (x^{\frac{1}{3}} y)$ .

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