Write as a Single Logarithm natural log of x+2 natural log of y- natural log of z

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

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

$2 \ln (y) + \ln (\frac{x}{z})$

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

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

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

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

Combine $y^{2}$ and $\frac{x}{z}$ .

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