# How do you evaluate log 900 - log 9?

Nov 6, 2016

This can be simplified to $2$.

#### Explanation:

By the rule ${\log}_{a} \left(n\right) - {\log}_{a} \left(m\right) = {\log}_{a} \left(\frac{n}{m}\right)$, we have:

$\log 900 - \log 9 = \log \left(\frac{900}{9}\right) = \log 100$

Since the notation $\log a$ is a logarithm in base $10$, we can use the change of base formula to rewrite the following:

$= \log \frac{100}{\log} 10 = \log {10}^{2} / \log 10 = \frac{2 \log 10}{\log} 10 = 2$

Hopefully this helps!