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The number of integers satisfying the in...

The number of integers satisfying the inequality `log_(sqrt(0.9))log_(5)(sqrt(x^(2)+5+x))gt 0` is

A

6

B

7

C

8

D

9

Text Solution

Verified by Experts

The correct Answer is:
C
`log_(sqrt(0.9))log_(5)(sqrt(x^(2)+5+x))gt0`
`rArr 0 lt log_(5)(sqrt(x^(2)+5+x))lt 1`
`rArr 1lt (x^(2)+5+x)^(1//2)lt 5`
`rArr 1lt x^(2)+5+ x lt 25`
`rArr x^(2)+x-20 lt 0` (as `x^(2)+x+4 gt 0` for all real x)
`rArr (x+5)(x-4)lt 0`
`rArr x in (-5, 4)`
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