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

Question

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!

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Answer 1 · 2018-03-11T15:24:59

see below

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#

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#