the roots of the equation x power underroot x = (underroot x ) of whole power x
Ben111:
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X is 4. Solution is in the image. Another solution could be zero but powers of zero aren't defined, so only root is 4.
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x^(√x) =(√x)^x
take log base x both side ,
√x = x/2
take square both side
x = x^2/4
x( 1 - x/4) =0
x =0, 4
but x ≠ 0 because if x =0 then log undefined so, x = 4
take log base x both side ,
√x = x/2
take square both side
x = x^2/4
x( 1 - x/4) =0
x =0, 4
but x ≠ 0 because if x =0 then log undefined so, x = 4
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