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

Question

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.

Answer 1

1

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)

posted Jul 25 '12

achrzesz
1661 ● 4 ● 16 ● 36

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 (Jul 25 '12)

Answer 2

0	`sage: l=e^(1/2x)+e^x sage: var('u') u sage: lu=l.subs(x=2log(u)) sage: assume(u>0) sage: solve(lu==2,u) [u == 1] sage: 2log(1) 0` link posted Jul 25 '12* achrzesz 1661 ● 4 ● 16 ● 36

2 Answers: