# How do you solve for x in  2^ logx = 1/4?

Dec 22, 2015

$x = 0.01$

#### Explanation:

Note that
$\textcolor{w h i t e}{\text{XXX}} \frac{1}{4} = \frac{1}{{2}^{2}} = {2}^{- 2}$

So if ${2}^{\log \left(x\right)} = \frac{1}{4}$
then
$\textcolor{w h i t e}{\text{XXX}} \log \left(x\right) = - 2$

$\textcolor{w h i t e}{\text{XXX}} {10}^{- 2} = x$ (based on definition of log)

$\textcolor{w h i t e}{\text{XXX}} x = \frac{1}{100} = 0.01$