Simplify/Condense 2 natural log of 4+3 natural log of x-4 natural log of y

$2 \ln (4) + 3 \ln (x) - 4 \ln (y)$

Simplify each term.

Simplify $2 \ln (4)$ by moving $2$ inside the logarithm.

$\ln (4^{2}) + 3 \ln (x) - 4 \ln (y)$

Raise $4$ to the power of $2$ .

$\ln (16) + 3 \ln (x) - 4 \ln (y)$

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

$\ln (16) + \ln (x^{3}) - 4 \ln (y)$

Simplify $- 4 \ln (y)$ by moving $4$ inside the logarithm.

$\ln (16) + \ln (x^{3}) - \ln (y^{4})$

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

$\ln (16 x^{3}) - \ln (y^{4})$

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

$\ln (\frac{16 x^{3}}{y^{4}})$