If `xy^(2) = 4 and log_(3) (log_(2) x) + log_(1//3) (log_(1//2) y)=1` , then `x` equals

Options

A. 4
B. 8
C. 16
D. 64

Answer

D

Explanation

`log_(3)(log_(2)x)+log_(1//3)(log_(1//2)y)= 1`
`or log_(3)(log_(2)x)-log_(3)(log_(1//2)y) = 1`
` or log_(3)(log_(2)(4//y^(2)))-log_(3)(log_(1//2)y) = 1`
` or log_(2)(4//y^(2))=3(log_(1//2)y)`
` or log_(2)(4//y^(2))=- 3 (log_(2)y)`
`or log_(2)(4//y^(2))+(log_(2)y^(3))=0`
` or 4y = 1`
` or y = 1//4`
` rArr x = 64`