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If log(1//2)(4-x)gelog(1//2)2-log(1//2)...

If ` log_(1//2)(4-x)gelog_(1//2)2-log_(1//2)(x-1)`,then x belongs to

A

`(1, 2]`

B

`[3, 4)`

C

`(1, 3]`

D

`[1, 4)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`log_(1//2)(4-x) ge log_(1//2)2-log_(1//2) (x-1)`
`or log_(1//2)(4-x)(x-1) ge log_(1//2) 2`
` or (4-x)(x-1) le 2`
` or x^(2) - 5x + 6 ge 0`
` or (x-3)(x-2) ge 0`
` or x ge 3 or x le 2`
But ` x in (1, 4)`
` rArr x in (1, 2] cup [3, 4)`
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