Question

The number of solutions of the equation
`x^("log"sqrt(x)^(2x)) =4` is

Answer 1

Correct Answer - A
The given equation is meaningful, if `x gt0 " and " x ne 1`.
Now,
`x^("log"sqrt(x)2x) = 4`
`rArr x^(2 "log"_(x)2x) = 4 rArr x^("log"_(x) 4x^(2)) = 4 rArr 4x^(2) = 4 rArr x = +-1`
But `x gt 0 " and " x ne 1`
Hence, the given equation has no solution.