Or you could use the LambertW function. Maple gives
> solve(exp(x*(x-3))=2*(x-1)*(x-2),x);
3/2+(1/2)*sqrt(1-4*LambertW(-(1/2)*exp(-2))), 3/2-
(1/2)*sqrt(1-4*LambertW(-(1/2)*exp(-2))),
3/2+(1/2)*sqrt(1-4*LambertW(-1, -(1/2)*exp(-2))), 3/2-
(1/2)*sqrt(1-4*LambertW(-1, -(1/2)*exp(-2)))
from ?LambertW:
•The LambertW function satisfies
LambertW(x) * exp(LambertW(x)) = x .
•As the equation y exp(y) = x has an infinite number of solutions y
for each (non-zero) value of x, LambertW has an infinite number of
branches. Exactly one of these branches is analytic at 0. In Maple
this branch is referred to as the principal branch of LambertW, and is
denoted by LambertW(x). The other branches all have a branch point at
0, and these branches are denoted in Maple by LambertW(k, x), where k
is any non-zero integer. (The principal branch can also be referred to
as LambertW(0, x)).
See also http://en.wikipedia.org/wiki/Lambertw
I am surprized that mathematica does not use it.
It doesn't look like SymPy has the LambertW function, unless I am
missing it.
Aaron Meurer
On Jun 24, 2009, at 10:20 AM, Alan Bromborsky wrote:
>
> Ondrej Certik wrote:
>> On Wed, Jun 24, 2009 at 6:18 AM, Sebastian
>> Haase<seb.ha...@gmail.com> wrote:
>>
>>> On Wed, Jun 24, 2009 at 11:06 AM, smichr <smi...@gmail.com> wrote:
>>>
>>>> If someone has access to Mathematica, could you see if it solves
>>>> the
>>>> equation,
>>>>
>>>> exp(x*(x-3))=2*(x-1)*(x-2)
>>>>
>>>> The Web-mathematica doesn't
>>>> (at
>>>> http://72.3.253.76/webMathematica3/quickmath/page.jsp?s1=equations&s2=solve&s3=basic)
>>>> and I'm wondering if a current version recognizes the solution or
>>>> not.
>>>>
>>>>
>>> I'm generally no Mathematica user, but I got this answer:
>>>
>>> Solve[Exp[x*(x - 3)] == 2*(x - 1)*(x - 2), x]
>>>
>>> Solve::tdep: The equations appear to involve the variables to be
>>> solved for in an essentially non-algebraic way.
>>>
>>
>> http://www.wolframalpha.com/input/?i=exp(x*(x-3))%3D2*(x-1)*(x-2)
>>
>> Ondrej
>>
>>>
>>
>>
> The equation reduces to exp(w) = 2*exp(2)*w where w = x*(x-3)+2.
> Wouldn't the solution of w have to be numerical?
> Is this what you are looking for?
>
> >
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