Solving w e^x

1. May 26, 2005

Guero

how do i solve
$$e^x+e^{3x}-1=0$$
for x?

2. May 26, 2005

exequor

to make it simple let y=e^x

thus giving y^3 + y - 1 = 0
y(y^2 + 1) = 1

i looked at this quickly and i don't think that you would get a solution for x.

Last edited: May 26, 2005
3. May 26, 2005

HallsofIvy

Staff Emeritus
Let y= ex and the equation becomes y3+ y- 1= 0. Can you solve that?

4. May 26, 2005

Guero

how can the answer be x=0?
$$e^{x}+e^{3x}-1=0$$
$$e^{0}+e^{3\times{0}}-1=0$$
$$1+1-1=0$$
$$1=0$$??

5. May 26, 2005

exequor

the answer cannot be zero, i edited my post (sorry about that)

6. May 26, 2005

Guero

no prob, but is there really no solution?

7. May 26, 2005

exequor

well it makes sense to me because this is a cubic function right? how did you go about solving for y?

8. May 26, 2005

Guero

i didn't, i don't know how to

9. May 26, 2005

Zurtex

There is 1 real answer and 2 initial complex answers, being non-simple roots of the cubic equation they all look quite nasty.

10. May 26, 2005

Guero

could someone explain how to find the real answer?

11. May 26, 2005

dextercioby

Check out Mathworld's page on the cubic equation.

Daniel.

12. May 26, 2005

Guero

ok, thanks

13. May 27, 2005

closure

you can set
$$y=e^x$$
then the equation will become $$y+y^3-1=0$$
now you can creat the term $$y^2$$,then minus the same term.