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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

[1,3]

C

[3,4)

D

[2,3]

Text Solution

Verified by Experts

The correct Answer is:
A, C
We have `log_(1//2)(4-x)ge log_(1//2)2-log_(1//2)(x-1)`
It is defined if `4-x gt 0` and `x- 1 gt 0` or `1 lt x lt 4` …..(i)
`rArr log_(1//2)(4-x)(x-1)ge log_(1//2)2`
`rArr (4-x)(x-1)ge 2`
`rArr x^(2)-5x + 6 ge 0`
`rArr (x-3)(x-2)ge 0`
`rArr x ge 3` or `x le 2` ......(ii)
From (i) and (ii), we get `x in (1,2] uu [3,4)`
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