Math Is Fun Forum
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#1 2014-08-09 05:31:17
Exponential Equation
How do you solve x^2 - 1 == 2^x ?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#2 2014-08-09 05:43:50
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Exponential Equation
Have you not heard of Abel?
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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#3 2014-08-09 06:01:46
Re: Exponential Equation
The one from Bible?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#4 2014-08-09 06:09:42
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Exponential Equation
Nope. Why do you expect an algebraic solution to this and not a numerical one?
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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#5 2014-08-09 06:21:28
Re: Exponential Equation
I have already seen the numerical one. I was looking for an algebraic or a so called 'elegant' method. Do not get me wrong. I have full faith in your methods.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#6 2014-08-09 06:26:33
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Exponential Equation
They are not my methods.
When integrating it is better to look for things which you can integrate rather than things which you cannot.
Why did you say that?
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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#7 2014-08-09 06:30:43
Re: Exponential Equation
It is a stupid quote, I agree
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#8 2014-08-09 06:38:56
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Exponential Equation
Nope, there is truth in it. The methods you have learned and are showing only do a small fraction of definite integrations. Most can not be done by those methods. The numerical methods do almost all of them. The ones we are taught in school and books can actually be thought of as mere tricks since they only work on a small subset of integrals. The numerical methods are the elegant ones, and the manipulation methods are anomalies. Same with root finding! The numerical methods do almost all while the algebraic can not even do all polynomials! Yet, we are given the impression that those ugly formulas for cubics and quartics are beautiful!
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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#9 2014-08-09 06:43:27
Re: Exponential Equation
I have already seen the numerical solution and I want to see an algebraic one now. Even if it is inferior or something, What is wrong with willing to see it?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#10 2014-08-09 06:50:25
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Exponential Equation
You are missing the point. It probably does not exist! The algebraic methods are only for contrived problems. If someone presents you with a school problem or a book one then look for an algebraic idea. But when you make one up, the chances are thousands to one no algebraic solutions exist.
You have not seen the numerical solutions because there are an infinite number of them. That is their power.
x = 3.000000000000000000000000000000000...
x = 3.407450522185998622022898453544828351981500456552533237669534056893008767412879...
x = -1.198250197036042778794136287877829569504868539187225014...
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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#11 2014-08-09 06:59:15
Re: Exponential Equation
The question is about beauty, not power.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#12 2014-08-09 07:00:54
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Exponential Equation
Do you find it beautiful to search for things that are not there. Algebraic methods are for polynomials. Is that a polynomial?
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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#13 2014-08-09 07:04:51
Re: Exponential Equation
It is not.
I do not know what is an 'algebraic method'. I opened this thread to see if someone has a solution which I think is beautiful. I am not sure what exactly it is.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#14 2014-08-09 07:06:55
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Exponential Equation
This is beautiful.
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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#15 2014-08-09 07:08:25
Re: Exponential Equation
It is called Newton-raphson.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#16 2014-08-09 07:10:35
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Exponential Equation
Yea, and it does lots of them.
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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#17 2014-08-09 07:13:07
Re: Exponential Equation
It is beautiful but I want some more beauty.
You do not like Newton-Raphson.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#18 2014-08-09 07:18:05
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Exponential Equation
It is beautiful but I want some more beauty.
Kaboobly doo! You have been trained to believe in an archaic concept of beauty.
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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#19 2014-08-09 07:21:53
Re: Exponential Equation
Concept of beauty is personal.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#20 2014-08-09 07:23:15
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Exponential Equation
Nothing unreal exists.
I will watch this thread eagerly to see a classically elegant answer come forth but it will not come from me.
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.
Offline
#21 2014-08-09 07:29:03
Re: Exponential Equation
The quote is hard to parse.
I doubt if anyone will read this thread at all
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#22 2014-08-09 07:36:09
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Exponential Equation
I doubt they will come up a solution that ain't numerical and you can take that to bank.
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.
Offline
#23 2014-08-09 07:39:22
Re: Exponential Equation
I do not know what is the difference between a numerical and a non-numerical solution.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#24 2014-08-09 07:47:17
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Exponential Equation
Prejudice is the difference.
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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#25 2014-08-09 07:54:09
Re: Exponential Equation
There can be a numerical solution I like too.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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