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How many integer values of x satisfy the...

How many integer values of `x` satisfy the inequality `(32)/(243) lt ((2)/(3))^(x^(2)) lt (9)/(4) ((8)/(27))^(x)`

A

`3`

B

`4`

C

`0`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
A
`((2)/(3))^(5) lt ((2)/(3))^(x^(2)) lt ((2)/(3))^(-2) lt ((2)/(3))^(3x)`
`rArr x^(2) lt 5` and `x^(2) gt -2 + 3x`
`sqrt5 lt x lt sqrt(5) cap x^(2) - 3x + 2 gt 0`
`(x - 2) ( x- 1) gt 0`
`x lt 1 cup x gt 2`
so `(-sqrt(5) lt x lt 1) cup (2 lt x lt sqrt5)`
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