InterviewSolution
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InterviewSolution
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Solve `x^((log)_y x)=2a n dy^((log)_x y)=16`A. ` 2^(root(3)2)`B. ` 2 ^(root(3)4)`C. ` 2 ^(root(3)128)`D. ` 2 ^(root(3)16)` |
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Answer» Correct Answer - D Let ` log_(y) x = 1` Then ` x = y^(t)` …(1) Now, ` x^(log_(y) x) =2` becomes ` x^(t) = 2` `rArr x = 2^(1//t)` …(2) And `y^(log_(x)y) = 16` becomes ` y^(1//t) = 2^(4)` ` rArr y = 2^(4//t)` ….(3) Putting the values of x and y in (1), we get ` 2^(1//t) = 2^(4t^(2))` ` rArr 4t^(3) = 1` ` :. t = (1/4)^(1//3)` ....(4) Using (4) and (2), we get ` x = (2)^((4)^(1//3)) = 2^(root(3)4)` Using (4) and (3), we get ` y = (2)^((4)^(2//3)) = 2^(root(3)16)` |
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