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#1 2010-04-04 00:15:12
- ZHero
- Real Member
- Registered: 2008-06-08
- Posts: 1,889
how to solve..
how can i solve
without plotting or programming??
If two or more thoughts intersect, there has to be a point!
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#2 2010-04-04 01:04:34
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: how to solve..
Hi ZHero;
You are being too restrictive. Those 2 techniques are powerful methods in themselves. The solution to that equation is the not too well known Lambert function or product log. The only methods that can work here are numerical ones.
1) iteration with Taylor series.
2) Newtons iteration.
3) Interval bisection
4) Dozens more.
They are all tedious to do without a computer but not impossible.
This I believe is the only real root. There may be complex roots.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#4 2010-04-04 01:38:29
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: how to solve..
Hi ZHero;
I don't think so. Doc mentions my 2 and 3. I wouldn't use false position (secant method, regula falsi) as it's convergence rate is inferior to newtons.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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