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

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

Step 1

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.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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