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Consider the system of equations log(...

Consider the system of equations
` log_(3)(log_(2)x)+log_(1//3)(log_(1//2)y) =1 and xy^(2) = 9`.
The value of x in the interval

A

`(200, 300)`

B

` (400, 500)`

C

`(700, 800)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`log_(3)(log_(2)x)+log_(1//3)(log_(1//2)y) = 1`
` rArr log_(3) (log_(2)x)-log_(3)(-log_(2)y) = 1`
` rArr log_(3)(-(log_(2)x)/(log_(2)y)) = 1`
` rArr -(log_(2)x)/(log_(2)y) = 3`
` rArr xy^(3) = 1`
Also, ` xy^(2) = 9`
` rArr y = 1/9`
` :. x = 729`
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