Question 137920: Please help me solve this question: -
Log base 1/2(x-1)>0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Log base 1/2(x-1)>0
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First: Note that x-1 must be > 0; i.e. x > 1
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Find the boundary point for the inequality:
log(1/2) (x-1) = 0
x-1 = (1/2)^0
x-1 = 1
x = 2
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Check a test point from the left interval and from the right interval.
If x = 3, log(1/2) (2) > 0, this is false so no solutions in (2,+inf)
If 1 < x < 2; pick x=3/2: log(1/2) (3/2-1) = 1 > 0 , so there are
solutions in 1 < x < 2
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Final Answer: 1 < x < 2
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Cheers,
Stan H.
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