Solving x²=-1/2ln(x) with x in (0,2]

[Paragon]

Hi,

so, I can't solve the embarissing:

x^{2} = -\frac{1}{2}ln(x)

, where x \in ]0, 2] or (0 < x \geq 2 )

any hep would be nice...
thanx for your pacience!

 

[iNCREDiBLE]

Paragon: Equations of this kind can't be solved exactly, i.e the solutions can't be expressed in elementary functions. You can use a numerical method, such as Newton's Method, to approximate the solution.

 

[amcavoy]

http://mathworld.wolfram.com/LambertW-Function.html

 

[sandeep]

Hi, why don't you try with Wright omega function it suits your requirement

y+lny=z
or as suggested by others use LambertW function