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Question

If log1/2(4x)log1/22log1/2(x1), then x

A
(1,2]
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B
[3,4)
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C
(1,3]
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D
[1,4)
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Solution

The correct option is B [3,4)
log1/2(4x)log1/22log1/2(x1)
For log to be defined,
4x>0 and x1>0
x(1,4) (1)

Now, log1/2(4x)log1/22log1/2(x1)
log2(4x)log22+log2(x1)log2(x1)+log2(4x)1log2[(x1)(4x)]1x2+5x42x25x+60x(,2][3,) (2)

From (1) and (2),
x(1,2][3,4)

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