Question 5155
 Given ln(x)^(ln(x))=4 
 Let y = ln x, the equation becomes

 y^y = 4,

 But y^y = 2^2, [This is the point: to take advantage 4 = 2^2]
 so y = 2 = ln x,
 We get x = e^2

 It seems a little tricky. While there is no other good
 ways even though I have tried to take ln , log2 , etc.
 
 Your idea is good, but not working for solving this tricky problem.

 Kenny