# How do you write an equation of a line going through (1/2)^x =16^2?

Nov 23, 2016

$x = - 8$

#### Explanation:

$\frac{1}{2} = {2}^{- 1}$

$\Rightarrow {\left(\frac{1}{2}\right)}^{x} = {\left({\left(2\right)}^{- 1}\right)}^{x} = {2}^{- x}$

$16 = {2}^{4}$

$\Rightarrow {16}^{2} = {\left({2}^{4}\right)}^{2} = {2}^{8}$

Therefore
$\textcolor{w h i t e}{\text{XXX}} {\left(\frac{1}{2}\right)}^{x} = {16}^{2}$

$\Rightarrow {2}^{- x} = {2}^{8}$

$\Rightarrow x = - 8$