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
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)`
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Correct Answer - 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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