Question

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) `(1/4)^x` < `1/8`

2) `(1/4)^x` > `1/8`

Thanks so much!

Answer 1

see below

Explanation:

1)
reduce the fractions to powers of 2

that is
`(1/2^2)^x < 1/2^3`

=

`1/2^(2x) < 1/2^3`

now just use the reciprocal and negate the powers

therefore,

`2^(-2x) < 2^-3`
therefore,

`-2x < -3`

`-x < -3/2`

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

therefore
1) `x > 3/2`
=
this is the answer for the first question and the second question is just the same whose answer is

2) `x < 3/2`