If ` log_(1//2)(4-x)gelog_(1//2)2-log_(1//2)(x-1)`,then x belongs toA. `(1, 2]`B. `[3, 4)`C. `(1, 3]`D. `[1, 4)`

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

1.	If ` log_(1//2)(4-x)gelog_(1//2)2-log_(1//2)(x-1)`,then x belongs toA. `(1, 2]`B. `[3, 4)`C. `(1, 3]`D. `[1, 4)`
Answer» Correct Answer - 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)`