# How do you solve these 2 inequalities? (Exponential function)

## Ok so I'd like an explanation (for one or both) with the answer as well for these 2 problems, please. 1) ${\left(\frac{1}{4}\right)}^{x}$ < $\frac{1}{8}$ 2) ${\left(\frac{1}{4}\right)}^{x}$ > $\frac{1}{8}$ Thanks so much!

Mar 11, 2018

see below

#### Explanation:

1)
reduce the fractions to powers of 2

that is
${\left(\frac{1}{2} ^ 2\right)}^{x} < \frac{1}{2} ^ 3$

=

$\frac{1}{2} ^ \left(2 x\right) < \frac{1}{2} ^ 3$

now just use the reciprocal and negate the powers

therefore,

${2}^{- 2 x} < {2}^{-} 3$
therefore,

$- 2 x < - 3$

# $- x < - \frac{3}{2}$

now when you revert these back to positive, the $<$ sign changes to the $>$ sign

therefore
1) $x > \frac{3}{2}$
=
this is the answer for the first question and the second question is just the same whose answer is

2) $x < \frac{3}{2}$