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Number of integers satisfying the inequa...

Number of integers satisfying the inequality `log_((x + 3)//(x - 3))4 lt 2 [log_(1//2)(x - 3)-log_(sqrt(2)//2)sqrt(x + 3)]` is greater than (A)`6` (B)`5` (C)`4` (D) `3`

A

`6`

B

`5`

C

`4`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
C, D
`x gt 3`
`log_((x + 3)/(x - 3)) 2 glt log_(2)'(x + 3)/(x - 3)`
Let `log_(2)'(x + 3)/(x - 3) = t`
`(1)/(t) lt 1 rArr x gt 3`
`t^(2) gt 1`
`rArr t gt 0 rArr gt 0`
`log_(2)'(x + 3)/(x - 3) gt 1`
`(x + 3)/(x - 3) gt 2 rArr x + 3 gt 2x - 6 rArr x lt 9`
so `3 lt x lt 9`
integral values `= 5`
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