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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 1/y lies in the interval

A

`(5, 7)`

B

`(7, 10)`

C

`(11, 15)`

D

`(25, 30)`

Text Solution

Verified by Experts

The correct Answer is:
B
`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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