Number of integral values of x which satisfying the equation, `9^(log_(3)(log_(2)x))=log_(2)x-(log_(2)x)^(2)+1` is :

Options

A. 1
B. `1//2`
C. 3
D. none of these

Answer

D

Explanation

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`