Simplify/Condense 3 natural log of x+9 natural log of y

$3 \ln (x) + 9 \ln (y)$

Step 1

Simplify each term.

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

$\ln (x^{3}) + 9 \ln (y)$

Simplify $9 \ln (y)$ by moving $9$ inside the logarithm.

$\ln (x^{3}) + \ln (y^{9})$

Step 2

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

$\ln (x^{3} y^{9})$