Solve $x^sqrtx = 16$ ?

Question

1335 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-06T09:45:02

$x=4$

Making $y = sqrt(x)$ we have

$(y^2)^y=y^(2y)=4^2$ so $y^y=4$

so $y = 2$

and $x = y^2= 4$

Now using the Lambert function $W$ we have

$y = log(4)/(W(log(4)))$ and also

$x = y^2=(log(4)/(W(log(4))))^2 = 4$

Solve x^sqrtx = 16x^sqrtx = 16 ?