# How do I solve log_sqrt50.2?

Oct 14, 2017

$- 2.$

#### Explanation:

We know that, ${\log}_{a} y = x \iff {a}^{x} = y .$

$\text{So, if, "log_sqrt5 0.2=x," then, } {\left(\sqrt{5}\right)}^{x} = 0.2 .$

$\therefore {\left({5}^{\frac{1}{2}}\right)}^{x} = 0.2 = \frac{2}{10} = \frac{1}{5.}$

$\therefore {5}^{\frac{x}{2}} = {5}^{- 1} .$

$\therefore \frac{x}{2} = - 1.$

$\therefore x = - 2.$

$\Rightarrow {\log}_{\sqrt{5}} 0.2 = - 2.$