Comments on: Is it possible to solve for X?
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X/
Comments on Ask MetaFilter post Is it possible to solve for X?Wed, 25 Apr 2012 14:45:27 -0800Wed, 25 Apr 2012 14:56:47 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Question: Is it possible to solve for X?
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X
<strong>(Y)(S^N) = (M)(X^(N+E)) - (Y)(X^N)</strong> Is it possible to solve for X? <br /><br /> I'm working on a manuscript (psychophysics), and it would be nice if I could solve for X in the following equation:<br>
<br>
(Y)(S^N) = (M)(X^(N+E)) - (Y)(X^N)<strong><br>
</strong><br>
the damn E term seems to be ruining things. Without it, it's simple enough.<br>
<br>
My math isn't the greatest, so I could really use some help!<br>
<br>
thanks!post:ask.metafilter.com,2012:site.213821Wed, 25 Apr 2012 14:45:27 -0800spacedivermathequationsalgebraresolvedBy: vacapinta
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085277
No, I don't think so. You have a general polynomial equation, that's all. <a href="http://mathworld.wolfram.com/AbelsImpossibilityTheorem.html">Abel's Impossibility theorem</a> severely restricts any algebraic solution unless you put restrictions on the values of N and E ( as you did by setting E=0)comment:ask.metafilter.com,2012:site.213821-3085277Wed, 25 Apr 2012 14:56:47 -0800vacapintaBy: spacediver
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085316
What if I set E to 0.5 (while leaving N as a variable), would it be possible then?comment:ask.metafilter.com,2012:site.213821-3085316Wed, 25 Apr 2012 15:26:15 -0800spacediverBy: spacediver
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085323
actually, I just realized I have values for N, E, S, and M. But I sense, based on my doodlings, that it's still impossible.comment:ask.metafilter.com,2012:site.213821-3085323Wed, 25 Apr 2012 15:32:08 -0800spacediverBy: oracle bone
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085331
Are the constants (specifically N,E) whole numbers? If so, does N+E<5>
<br>
(Also, do you need an equation or to solve for specific values? Could you try solving for Y in terms of X and then graphing it?)</5>comment:ask.metafilter.com,2012:site.213821-3085331Wed, 25 Apr 2012 15:41:34 -0800oracle boneBy: dness2
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085332
Actually, I think you can. Use natural logs on both sides then I think you can work the algebra so lnX is all by itself.<br>
I'm supposed to be finishing my term grades so I can't really finish it up, but I think it works from there.comment:ask.metafilter.com,2012:site.213821-3085332Wed, 25 Apr 2012 15:41:42 -0800dness2By: oracle bone
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085333
Sorry, that was supposed to say "N+E<5?"comment:ask.metafilter.com,2012:site.213821-3085333Wed, 25 Apr 2012 15:42:06 -0800oracle boneBy: Obscure Reference
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085340
Do you want a numerical solution? That should be possible if you have all the other values. What you can't get (in general) is an analytic solution in closed form.comment:ask.metafilter.com,2012:site.213821-3085340Wed, 25 Apr 2012 15:47:02 -0800Obscure ReferenceBy: spacediver
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085342
oracle: the constants are not integers, but they're all positive values. N + E does add up to less than 5.<br>
<br>
I've already graphed Y in terms of X, so I could do it crudely to look up specific values, but would be ideal to be able to graph X in terms of Y based on a continuous function.<br>
<br>
dness: thanks for the suggestion, but I barely understand the natural logarithmcomment:ask.metafilter.com,2012:site.213821-3085342Wed, 25 Apr 2012 15:47:51 -0800spacediverBy: spacediver
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085347
obscure: not quite sure what you mean. What i need to be able to do is to plot X as a function of [(Y+1) - (Y)]comment:ask.metafilter.com,2012:site.213821-3085347Wed, 25 Apr 2012 15:49:56 -0800spacediverBy: zeptoweasel
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085365
Are you sure? Because (Y+1)-(Y)=1. Plotting X as a function of 1 doesn't make sense.comment:ask.metafilter.com,2012:site.213821-3085365Wed, 25 Apr 2012 16:07:20 -0800zeptoweaselBy: spikeleemajortomdickandharryconnickjrmints
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085389
What they mean by natural log is this.<br>
<br>
Y^X = A<br>
ln(Y^X) = ln(A)<br>
X*ln(Y) = ln (A)<br>
X = [ln(A)] ÷ [ln(Y)]<br>
<br>
The trick here is that ln(Y^X) is the same as X*ln(Y).comment:ask.metafilter.com,2012:site.213821-3085389Wed, 25 Apr 2012 16:28:13 -0800spikeleemajortomdickandharryconnickjrmintsBy: spikeleemajortomdickandharryconnickjrmints
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085394
Oh, and this works for any log base, not just natural log.<br>
<br>
So log(Y^X) = X*log(Y).comment:ask.metafilter.com,2012:site.213821-3085394Wed, 25 Apr 2012 16:29:14 -0800spikeleemajortomdickandharryconnickjrmintsBy: spikeleemajortomdickandharryconnickjrmints
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085396
<small>And just looking at it, 1 minute before class starts, it seems to me that you <em>can</em> solve for X. I'll break out a pen and paper when I'm out of class and let you know if I solve it.</small>comment:ask.metafilter.com,2012:site.213821-3085396Wed, 25 Apr 2012 16:30:16 -0800spikeleemajortomdickandharryconnickjrmintsBy: spikeleemajortomdickandharryconnickjrmints
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085399
<small>Nope, I can't do it. Might be possible, but I'm not seeing it.</small>comment:ask.metafilter.com,2012:site.213821-3085399Wed, 25 Apr 2012 16:33:07 -0800spikeleemajortomdickandharryconnickjrmintsBy: spacediver
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085405
zepto: Y refers to a function there not a variable.<br>
<br>
spikelee: i see what u meancomment:ask.metafilter.com,2012:site.213821-3085405Wed, 25 Apr 2012 16:36:33 -0800spacediverBy: spacediver
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085410
zepto: to clarify:<br>
<br>
I need to solve for f(Y+1) - f(Y)comment:ask.metafilter.com,2012:site.213821-3085410Wed, 25 Apr 2012 16:41:21 -0800spacediverBy: spacediver
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085425
thanks for all the help here, I really appreciate it. I'm gonna try the crude approximation method - should be good enough :)comment:ask.metafilter.com,2012:site.213821-3085425Wed, 25 Apr 2012 17:03:49 -0800spacediverBy: triggerfinger
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085466
I am not a math person. Is there any reason you can't plug in numbers and simplify?<br>
<br>
(Y)(S^N) = (M)(X^(N+E)) - (Y)(X^N)<br>
<br>
If:<br>
y=5<br>
s=3<br>
n=2<br>
m=10<br>
e=1<br>
<br>
so:<br>
<br>
(5)(3^2) = (10)(X^(2+1)) - (5)(X^2)<br>
<br>
=(5)(3^2) = (10)(x^3)-(5)(x^2)<br>
= 5(9) = 10x^3 - 5x^2<br>
= 45 = 10-5 (x^3)(x^2)<br>
= 45 = 5x^5<br>
= 9 = x^5<br>
= 9^.20 = x<br>
=1.55 = xcomment:ask.metafilter.com,2012:site.213821-3085466Wed, 25 Apr 2012 17:39:27 -0800triggerfingerBy: spacediver
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085486
trigger: that would work if i were looking for the value of x at a particular y, but in my case, i need to find the value of x at any given y.<br>
<br>
Anyway, I've figured out the crude approximation solution and it works beautifully. <br>
<br>
<a href="http://www.mathworks.com/matlabcentral/fileexchange/2838-findnearest-m/content/findnearest.m">This</a> helped.comment:ask.metafilter.com,2012:site.213821-3085486Wed, 25 Apr 2012 17:56:11 -0800spacediverBy: dness2
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085488
I'm back. If I did it right the answer is:<br>
X=Y/M-[e^(N+E) /S^(N^2)]<br>
<br>
Like Spikeetc. Was saying, take the ln of both sides, get lnX by itself then raise both sides to e.comment:ask.metafilter.com,2012:site.213821-3085488Wed, 25 Apr 2012 17:56:49 -0800dness2By: flug
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085527
<a href="http://www.wolframalpha.com/input/?i=%28Y%29%28S%5EN%29+%3D+%28M%29%28X%5E%28N%2BF%29%29+-+%28Y%29%28X%5EN%29">Wolfram Alpha is always useful</a> if you've forgotten your math . . . <br>
<br>
(I changed E to F because W|A was interpreting E as the math constant <em>e</em>.)<br>
<br>
You can rather easily solve for Y--that might be useful.comment:ask.metafilter.com,2012:site.213821-3085527Wed, 25 Apr 2012 18:31:55 -0800flugBy: spacediver
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085694
wow...comment:ask.metafilter.com,2012:site.213821-3085694Wed, 25 Apr 2012 21:01:18 -0800spacediverBy: spacediver
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085722
dness: I don't think that's correct. When I plot X in terms of Y and compare Y in terms of X, they don't correspond.<br>
<br>
flug: that's a very nifty tool. I already have the solution for X in terms of Y though. The formulation in the original post was based on that original formulation - i had already done some re-arranging to make it more digestible.<br>
<br>
<br>
thank you both for the efforts though :)comment:ask.metafilter.com,2012:site.213821-3085722Wed, 25 Apr 2012 21:28:21 -0800spacediverBy: spacediver
http://ask.metafilter.com/213821/Is-it-possible-to-solve-for-X#3085724
dness, in case you were wondering, I checked both <br>
<br>
X=[Y/M]-[e^(N+E) /S^(N^2)]<br>
<br>
and<br>
<br>
X=Y/[M-[e^(N+E) /S^(N^2)]]comment:ask.metafilter.com,2012:site.213821-3085724Wed, 25 Apr 2012 21:29:05 -0800spacediver