# How do you condense log_2((8x^2)/y)+log_2(2xy)?

Jul 19, 2016

${\log}_{2} \left(16 {x}^{3}\right)$

#### Explanation:

If two log terms are being added, then it means that the numbers are being multiplied. The two terms can be written as the log of a single number. The bases of the logs are the same.

${\log}_{2} \left(\frac{8 {x}^{2}}{y}\right) + {\log}_{2} \left(2 x y\right)$

=${\log}_{2} \left[\frac{8 {x}^{2}}{y} \times 2 x y\right]$

=${\log}_{2} \left(16 {x}^{3}\right)$