# How do you calculate log _2 (1/8)?

Jul 27, 2016

-3

#### Explanation:

Let ${\log}_{2} \left(\frac{1}{8}\right) = n$ and we want to calculate the value of n.

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder}} \textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\log}_{b} x = n \Leftrightarrow x = {b}^{n}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

here b = 2 and x$= \frac{1}{8} \Rightarrow \frac{1}{8} = {2}^{n} \Rightarrow n = - 3$

Since ${2}^{-} 3 = \frac{1}{2} ^ 3 = \frac{1}{8}$

$\Rightarrow {\log}_{2} \left(\frac{1}{8}\right) = - 3$