# How do you evaluate  log_10 200 - log_10 2?

Mar 27, 2016

$2$

#### Explanation:

From the laws of logs we have that

${\log}_{a} x - {\log}_{a} y = {\log}_{a} \left(\frac{x}{y}\right)$

So in this particular case we get that

${\log}_{10} 200 - {\log}_{10} 2 = {\log}_{10} \left(\frac{200}{2}\right)$

$= {\log}_{10} 100$

$= 2$. (since ${10}^{2} = 100$)