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Prove that the equation x^(log(sqrtx^(2x...

Prove that the equation `x^(log_(sqrtx^(2x)))=4` has no solution.

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We have ` x^(log_(sqrtx^(2x)))=4, x gt 0 , x ne 1`
` rArr x ^(2 log_(x) 2x) = 4`
` rArr x^(log_(x)4x^(2))=4`
` rArr 4x^(2) = 4`
` rArr x = pm 1`,which is not possible.
Hence, equation has no solution.
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