how to solve: exp(x)+exp(1/2*x) == 2?

amalea
81 ●7 ●10 ●13

sage: assume(x,'real')
sage: solve(exp(x)+exp(-1/2*x) == 2,x)
[x == 2*log(1/2*sqrt(5) - 1/2), x == 0]

that ist ok!

how can i get here the solution x==0?

sage: solve(exp(x)+exp(1/2*x) == 2,x)
[e^x == -e^(1/2*x) + 2]

Thanks for help.

2 Answers

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achrzesz
2768 ●5 ●25 ●60

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)

Also see http://trac.sagemath.org/sage_trac/ticket/10444, which should be in Sage 5.3, for more obvious documentation of this option!

kcrisman ( 2012-07-26 00:11:24 +0100 )edit

achrzesz
2768 ●5 ●25 ●60

sage:  l=e^(1/2*x)+e^x
sage: var('u')
u
sage: lu=l.subs(x=2*log(u))
sage: assume(u>0)
sage: solve(lu==2,u)
[u == 1]
sage: 2*log(1)
0

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