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

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

Step 1

Simplify each term.

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

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

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

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

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

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

Step 2

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

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

Step 3

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

$\ln (\frac{x^{3} y^{2}}{z^{4}})$