# How do you solve 8 log_2 2-2log_2 8?

Nov 13, 2015

$8 {\log}_{2} 2 - 2 {\log}_{2} 8 = 2$

#### Explanation:

Evaluating ${\log}_{2} 2$ is equivalent to asking
$\textcolor{w h i t e}{\text{XXX}}$"For what value $p = {\log}_{2} 2$ is ${2}^{p} = 2$?"
The obvious answer is ${\log}_{2} 2 = p = 1$

Similarly, evaluating ${\log}_{2} 8$ is equivalent to asking
$\textcolor{w h i t e}{\text{XXX}}$"For what value $q = {\log}_{2} 8$ is ${2}^{q} = 8$?
with an obvious answer ${\log}_{2} 8 = q = 3$

So
$\textcolor{w h i t e}{\text{XXX}} 8 {\log}_{2} 2 - 2 {\log}_{2} 8$
$\textcolor{w h i t e}{\text{XXXXXX}} = 8 \times 1 - 2 \times 3$
$\textcolor{w h i t e}{\text{XXXXXX}} = 2$