= 0      (1)


     = 0      (2)


Introduce new variable t = e^x.

Then the equation (2)  takes the form


      = 0.       (3)


Apply the quadratic formula


     t =  = .


So, the equation (3) has two roots


       =   and   = .


Both the roots    and   are real numbers.


Since  t = , we can use ONLY POSITIVE root  to find x:


    x = .      ANSWER


It is the ONLY SOLUTION to the original equation (1).