math equation
Author  Topic: math equation 

Warrior
Member # 5483

written Friday, February 10 2006 23:03
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can someone please solve this equation? 59.7x^y = 35.9y^x  Ignorance Is bliss Cypher (Matrix) Don't think you can; know you can Morpheus (Matrix) sanity is overrated :) Posts: 130  Registered: Monday, February 7 2005 08:00 
Post Navel Trauma ^_^
Member # 67

written Saturday, February 11 2006 00:30
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Hooray for one equation in two unknowns.  Barcoorah: I even did it to a big dorset ram. desperance.net  Don't follow this link Posts: 1798  Registered: Thursday, October 4 2001 07:00 
Warrior
Member # 6714

written Saturday, February 11 2006 00:34
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... Err... Y=2 and X=7? Okay, I've failed. Anyone else?  Well that signature was out of date, since I've not been here in forever. Posts: 91  Registered: Thursday, January 19 2006 08:00 
Lifecrafter
Member # 3171

written Saturday, February 11 2006 00:39
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No way man. I'm in cabbage maths and my teacher is actually a wood work teacher. Gotta love the New Zealand education system. Posts: 776  Registered: Friday, July 4 2003 07:00 
Post Navel Trauma ^_^
Member # 67

written Saturday, February 11 2006 00:54
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I can see two obvious solutions, and there are bound to be a lot more. On the other hand, I prefer not to do other people's homework.  Barcoorah: I even did it to a big dorset ram. desperance.net  Don't follow this link Posts: 1798  Registered: Thursday, October 4 2001 07:00 
Infiltrator
Member # 2836

written Saturday, February 11 2006 02:01
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That's the type of homework you get? I would not like to be at your school. Posts: 587  Registered: Tuesday, April 1 2003 08:00 
Master
Member # 5977

written Saturday, February 11 2006 02:13
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What grade are you in!? I'm in fourth grade of secondary school (yes, that's the Dutch way of giving it names), and I didn't get those things yet.  Play and rate my scenarios: Where the rivers meet View my upcoming scenario: The Nephil Search: Escape. Give us your drek! Posts: 3029  Registered: Saturday, June 18 2005 07:00 
Law Bringer
Member # 2984

written Saturday, February 11 2006 02:14
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If this equation was given without additional information, then the one who gave it to you was either being a moron, messing with you, or asking you to solve for one in terms of the other. It so happens that Maple is your friend when it comes to math. Solving for y in terms of x: Where LambertW stands for Lambert's W Function. Instinctively, I'd say that if you had come across or understood that function (I haven't, and I study Math), you wouldn't need to post math questions on this forum... [ Saturday, February 11, 2006 02:17: Message edited by: Arancaytar the Grey ]  Encyclopaedia Ermariana • Forum Archives • Forum Statistics • RSS [Topic / Forum] My Blog • Polaris • I eat novels for breakfast. Polaris is dead, long live Polaris. Look on my works, ye mighty, and despair. Posts: 8752  Registered: Wednesday, May 14 2003 07:00 
Electric Sheep One
Member # 3431

written Saturday, February 11 2006 02:24
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There is a oneparameter family of solutions; what you can solve for is the functional form of y(x). That's rather a lady doggie, since it's a transcendental equation. This means that the answer just isn't any standard, known function; it's itself, and that's all you can say. If you really need to know y for arbitrary x, go numerical. That mean's plug it into a computer. Or, if you just want any one solution, pick either x or y to be something very convenient, like 1, to make the solution for the other variable easy. (I presume these are Khoth's two solutions.) EDIT: Huh, I stand corrected by Maple. The answer does involve a standard, known function  insofar as the LambertW function counts as standard and known. Sadly, applied math is full of hundreds of such obscure functions. Identifying one is really only helpful because (a) you may be able to look up some of its properties, because they were proven a hundred years ago by some obscure mathematician, and (b) modern software libraries know them by heart, and can plot them for you instantly. [ Saturday, February 11, 2006 02:28: Message edited by: Student of Trinity ]  We're not doing cool. We're doing pretty. Posts: 3335  Registered: Thursday, September 4 2003 07:00 
Law Bringer
Member # 2984

written Saturday, February 11 2006 04:13
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quote:Can it be solved analytically then? I'd say that's as good a criterion as any. The equation I posted above looks like it can only be approximated, but then, I basically suck at numerical math.  Encyclopaedia Ermariana • Forum Archives • Forum Statistics • RSS [Topic / Forum] My Blog • Polaris • I eat novels for breakfast. Polaris is dead, long live Polaris. Look on my works, ye mighty, and despair. Posts: 8752  Registered: Wednesday, May 14 2003 07:00 
Master
Member # 4614

written Saturday, February 11 2006 08:59
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Typing the equation in here will lead to a rather complicated and obviously approximate solution that is probably still pretty accurate.  ben4808 Posts: 3360  Registered: Friday, June 25 2004 07:00 
Law Bringer
Member # 335

written Saturday, February 11 2006 11:05
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I'd suspect a typo, but there's no obvious change to that equation that makes it reasonable to solve without outside aids but not trivial. —Alorael, who does not like solution that involve equations that must be looked up on Wikipedia. Posts: 14579  Registered: Saturday, December 1 2001 08:00 
Warrior
Member # 5483

written Sunday, February 12 2006 04:28
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quote:This isn't schoolwork actually and to answer Thralni's question, I'm a junior in high school.  Ignorance Is bliss Cypher (Matrix) Don't think you can; know you can Morpheus (Matrix) sanity is overrated :) Posts: 130  Registered: Monday, February 7 2005 08:00 
Shaper
Member # 32

written Sunday, February 12 2006 12:12
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59.7x^y = 35.9y^x x^y = (35.9)/(59.7)y^x Letting y = (59.7)/(35.9), x^y = y^(x1). Notice if x = 1, 1^y = 1 and y^(11) = 1. If you divide by 35.9 and follow the same process you'll arrive at the other solution that Khoth spoke of... [ Sunday, February 12, 2006 12:14: Message edited by: Lt. Sullust ]  Lt. Sullust Cogito Ergo Sum Polaris Posts: 2462  Registered: Wednesday, October 3 2001 07:00 
Law Bringer
Member # 2984

written Monday, February 13 2006 00:54
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So wait, the task was to find ONE solution, not all possible solutions? The difference in this case is comparable to the difference between calculating the first four digits of Pi and its exact value. :rolleyes:  Encyclopaedia Ermariana • Forum Archives • Forum Statistics • RSS [Topic / Forum] My Blog • Polaris • I eat novels for breakfast. Polaris is dead, long live Polaris. Look on my works, ye mighty, and despair. Posts: 8752  Registered: Wednesday, May 14 2003 07:00 