I need to solve a function for $x$


I know the solution(s) should be expressed using Lambert W function because the above function can also be expressed as


however, I cannot proceed any further.

  • $\begingroup$ $\log$ is base two, right? $\endgroup$ – Simply Beautiful Art Mar 17 '17 at 17:35
  • $\begingroup$ $\log$ is base 2. However I realize my mistake. I will edit the second line. $\endgroup$ – C.Koca Mar 17 '17 at 17:41

By log rules, we have


Multiply both sides by $x$ and square both sides:


Let $u=x^2$ to simplify:


Divide both sides by $2^{u+2k+1}$ and multiply both sides by $-\ln(2)$.


Take the $W$ of both sides to get



So finally,



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.