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If log(3)x-(log(3)x)^(2)le(3)/(2)log((1/...

If `log_(3)x-(log_(3)x)^(2)le(3)/(2)log_((1//2sqrt(2)))4`, then x can belong to

A

`(-oo,1//3)`

B

`(9,oo)`

C

(1,6)

D

`(-oo,0)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`log_(3)x-(log_(3)x)^(2)le(3)/(2)log_((1//2sqrt(2))4`
`rArr log_(3)x-(log_(3)x)^(2)le -2`
`rArr (log_(3)x)^(2)-log_(3)x-2 ge 0`
`rArr (log_(3)x-2)(log_(3)x+1)ge 0`
`rArr log_(3)x le -1` or `log_(3)x le 2`
`rarr le 1//3` or `x ge 9`
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