# How do you evaluate  log 300 - log 3?

Nov 4, 2015

Have a look:

#### Explanation:

I would use the property of logs that tells us:
$\log a \cdot b = \log a + \log b$
To get:
$\log \left(3 \cdot 100\right) - \log \left(3\right) =$
$= \log \left(3\right) + \log \left(100\right) - \log \left(3\right) =$
$= \cancel{\log 3} + \log \left(100\right) \cancel{- \log 3} =$
$= \log \left(100\right)$
If the base of the log is $10$ then:
${\log}_{10} \left(100\right) = 2$