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

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

Simplify each term.

Simplify $2 \log (x)$ by moving $2$ inside the logarithm.

$\log (x^{2}) + \log (y) - 2 \log (z)$

Simplify $- 2 \log (z)$ by moving $2$ inside the logarithm.

$\log (x^{2}) + \log (y) - \log (z^{2})$

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

$\log (x^{2} y) - \log (z^{2})$

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

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