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!

1 Answer
Mar 11, 2018

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