# How do you simplify logx^2-logxy+4logy?

Jul 15, 2016

$\log \left(\frac{{x}^{2} {y}^{4}}{x y}\right)$

#### Explanation:

$\log {x}^{2} - \log x y + 4 \log y$

3 log terms can be written as the log of a single term.

If logs are added, then the numbers are multiplied.
If logs are subtracted, then the numbers are divided.

$\log {x}^{2} - \log x y + 4 \log y = \log {x}^{2} - \log x y + \log {y}^{4}$

$\log \left(\frac{{x}^{2} {y}^{4}}{x y}\right)$