Write as a Single Logarithm 5 log of x+2 log of y- log of z

$5 \log (x) + 2 \log (y) - \log (z)$

Simplify each term.

Simplify $5 \log (x)$ by moving $5$ inside the logarithm.

$\log (x^{5}) + 2 \log (y) - \log (z)$

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

$\log (x^{5}) + \log (y^{2}) - \log (z)$

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

$\log (x^{5} y^{2}) - \log (z)$

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

$\log (\frac{x^{5} y^{2}}{z})$