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answered 2012-07-25 17:51:59 +0100
sage: solve(exp(x)+exp(1/2*x)==2,x,to_poly_solve=True) [x == 2*I*pi + 4*I*pi*z36 + 2*log(2), x == 4*I*pi*z38]
For z38=0, x=0
(Wolframalpha gives the same solution)