# How do you solve log_2 [2^(-13)]?

Mar 24, 2016

${\log}_{2} {2}^{-} 13 = - 13$

#### Explanation:

${\log}_{2} {2}^{-} 13 = - 13 \cdot {\log}_{2} 2$
${\log}_{2} 2 = 1$
${\log}_{2} {2}^{-} 13 = - 13 \cdot 1$
${\log}_{2} {2}^{-} 13 = - 13$

Mar 24, 2016

${\log}_{2} \left[{2}^{-} 13\right] = - 13$

#### Explanation:

It is important to remember that:
color(white)("XXX")color(red)(log_b a = c color(white)("XX") "means" color(white)("XX")b^c=a)

If
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{{\log}_{2} \left[{2}^{- 13}\right] = c}$
then we are asking for what value of $\textcolor{b l u e}{c}$ is
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{{2}^{c} = {2}^{- 13}}$

Hopefully the answer is clear that
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{c = - 13}$