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

Options

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

Answer

A, B

Explanation

`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)`