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The smallest integral x satisfying the i...

The smallest integral x satisfying the inequality `(1-log_(4)x)/(1+log_(2)x)le (1)/(2)x is.

A

`sqrt(2)`

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Let `log_(2)x=t`
`therefore (1-(t//2))/(1+t)le(1)/(2)`
`rArr (2-t)/(1+t)le 1`
`rArr (2-t)/(1+t)-1le 0`
`rArr (2t-1)/(t+1)ge 0`
`rArr t lt -1` or `t ge (1)/(2)`
`rArr log_(2)x gt-1` or `log_(2)x ge (1)/(2)`
`rArr 0 lt x lt (1)/(2)` or `x ge sqrt(2)`
`rArr` smallest integer is 2
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