# How do you simplify log 4 + log 5 - log 2?

Apr 8, 2018

To answer this question, the following logarithm rules are needed:
$\log a + \log b = \log \left(a \cdot b\right)$
$\log a - \log b = \log \left(\frac{a}{b}\right)$
${\log}_{b} b = 1$

Using the above rules:
$\log 4 + \log 5 - \log 2$
$= \log \left(\frac{4 \cdot 5}{2}\right)$
$= \log \left(\frac{20}{2}\right)$
$= \log \left(10\right)$
Since the base of a normal $\log$ is $10$, $\log 10 = 1$ (as ${10}^{1} = 10$).