# How do you condense 2 Log5 x - log5 y ?

Apr 11, 2016

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

#### Explanation:

Condense the first $\log$, using the law that a coefficient outside a logarithm is the same as a power inside.

$2 \log 5 x = \log 5 {x}^{2}$

Now condense everything, knowing that $\log a - \log b = \log \left(\frac{a}{b}\right)$.

$\log 5 {x}^{2} - \log 5 y = \log \left(\frac{5 {x}^{2}}{5 y}\right) = \log \left({x}^{2} / y\right)$