Question

Solve `x^sqrtx = 16` ?

Answer 1

`x=4`

Explanation:

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`