# How do you calculate log_2 4 - log_4 2?

Aug 1, 2016

${\log}_{2} 4 - {\log}_{4} 2$ $=$ $2 - \frac{1}{2}$ $=$ $\frac{3}{2}$

#### Explanation:

When I write ${\log}_{a} b$ $=$ $c$, in effect I ask to what power do I raise the base $a$ to get $b$.

By this definition, if ${\log}_{a} b$ $=$ $c$, then ${a}^{c} = b$.

Typically we use $\text{logs}$ to the base $10$ or the base $e$.

Can you tell me what is ${\log}_{10} 100 + {\log}_{10} 1000$ ?