Simplify/Condense 5 natural log of x-2 natural log of y

$5 \ln (x) - 2 \ln (y)$

Step 1

Simplify each term.

Simplify $5 \ln (x)$ by moving $5$ inside the logarithm.

$\ln (x^{5}) - 2 \ln (y)$

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

$\ln (x^{5}) - \ln (y^{2})$

Step 2

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

$\ln (\frac{x^{5}}{y^{2}})$