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If 9^("log"3("log"(2) x)) = "log"(2)x - ...

If `9^("log"_3("log"_(2) x)) = "log"_(2)x - ("log"_(2)x)^(2) + 1,` then x =

A

1

B

`1//2`

C

3

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`9^("log"3("log"_(2) x)) = "log"_(2)x - ("log"_(2)x)^(2) + 1`
`rArr 3^(2"log"_(3) ("log"_(2)x)) = "log"_(2) x - ("log"_(2)x)^(2) +1`
`rArr 3^("log"_(3) ("log"_(2) x)^(2)) = "log"_(2) x - ("log"_(2)x)^(2) + 1`
`rArr ("log"_(2) x)^(2) = "log"_(2)x - ("log"_(2)x)^(2) + 1`
`rArr 2("log"_(2) x)^(2) - "log"_(2) x - 1 =0`
`rArr (2"log"_(2) x +1) ("log"_(2)x-1) = 0`
`rArr "log"_(2)x = -(1)/(2), "log"_(2) x =1 rArr x = 2^(-1//2), 2`
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