Simplify/Condense 2 natural log of x-1/4 natural log of y

$2 \ln (x) - \frac{1}{4} \ln (y)$

Simplify each term.

Simplify $2 \ln (x)$ by moving $2$ inside the logarithm.

$\ln (x^{2}) - \frac{1}{4} \cdot \ln (y)$

Multiply $- \frac{1}{4} \ln (y)$ .

Reorder $\ln (y)$ and $\frac{1}{4}$ .

$\ln (x^{2}) - (\frac{1}{4} \ln (y))$

Simplify $\frac{1}{4} \ln (y)$ by moving $\frac{1}{4}$ inside the logarithm.

$\ln (x^{2}) - \ln (y^{\frac{1}{4}})$

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

$\ln (\frac{x^{2}}{y^{\frac{1}{4}}})$