Simplify/Condense 6 natural log of x-3 natural log of y

$6 \ln (x) - 3 \ln (y)$

Step 1

Simplify each term.

Simplify $6 \ln (x)$ by moving $6$ inside the logarithm.

$\ln (x^{6}) - 3 \ln (y)$

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

$\ln (x^{6}) - \ln (y^{3})$

Step 2

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

$\ln (\frac{x^{6}}{y^{3}})$