y^x = x^y

[fafalone]

So, can anyone solve for y in terms of x?

 

y^x=x^y

 

I sure can't solve it, and my TI-89 couldn't solve it either.

[Kedas]

if x=y is already one solution

I guess you already knew that one

[fafalone]

That's a specific solution, not the general solution.

[Kedas]

Yeah, I know

 

I was curious so I did search the internet a bit.

 

This could be a good start: (I can't read it)

http://www.zahlentheorie.de/forum/messages/618.html

 

 

If you want more brain trouble you can find that here:

http://www.mathematik.uni-bielefeld.de/~sillke/

solution : http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/x%5Ey-x%5Ey

[YT2095]

I`m no good at maths, but is the answer 1?

it`s seems to be the only number that wont perpetuate the problem.

[Kedas]

YT2095 said in post #5 :

I`m no good at maths, but is the answer 1?

Yes, together with all the other numbers you can think of (assuming y=x)

[YT2095]

but if x and y were the same then using 2 would make 4 throwing the rest of it out, it would just loop and get bigger.

whereas with 1 it can loop all it likes and X and Y can still be the same forever.

 

maybe I just understand the prob? I did say I was crap at maths

[Kedas]

Soo you are the one that invented loops ??

 

serious:

I have no idea what loops have to do with this equation.

 

It's like (but more complicated):

x^2=2Y what is X?

Answer X=SQRT(2Y)

[YT2095]

X~Y I can see

x=y doesn`t seem right somehow?

not in terms of real values other than 1.

 

the loop I saw as if x=y and y=2 then X^2=4, then wouldn`t it read as 4=2^y and since weve already established that, it would read as x^4=y^x and it would just get bigger?

 

but I pictured it in my head, so probably not the best place to work things out

actualy on a re read I must have been trippin, ignore it

 

Math`s aint ma strong point, but I thought I`de have a go anyway at the risk of PROOVING I`m lousey maths, as an oportunity to learn something

[Kedas]

examples:

Y=X=1 1^1=1^1 (1=1)

Y=X=2 2^2=2^2 (4=4)

Y=X=3 3^3=3^3 (27=27)

Y=X=4 4^4=4^4 (256=256)

Y<>X 2^4=4^2 (16=16)

 

Although I can imagine it is looping in your head

They say I have a lot of patience

[YT2095]

YUP!!! 100% that`s how I saw it

you just put it a kazillion times better than I could

it was a bit like a NOT gate that fed back to itself.

 

I still don`t get what use that equasion could be though or how it`s employed in maths? (never done any real Algebra other than Boolean).

 

and thnx for your patients

[NSX]

YT2095 said in post #11 :

YUP!!! 100% that`s how I saw it

you just put it a kazillion times better than I could

it was a bit like a NOT gate that fed back to itself.

 

I still don`t get what use that equasion could be though or how it`s employed in maths? (never done any real Algebra other than Boolean).

 

and thnx for your patients

 

You could do it trivially, but as you say, it goes on & on & ....

 

Check those sites that kedas posted; some of that stuff is over my head though

 

[Snorlax]

I think x^y=y^x could only work if x is a factor or multiple of y, and vice verse. But I am not sure........

[lqg]

i made a thread about this in physicsforums:

http://physicsforums.com/showthread.php?s=&threadid=4013

 

btw thanks kedas for the solution.

[Dave]

I certainly can't find a solution and I've been thinking about it for the best part of 2 days now

[YT2095]

Sweet! I don`t feel like such a "Dumb a$$" now if Dave can`t solve it

[Guest clifford zagnut]

let cp=x%(cp/z)+5y

[Dave]

?

[neo_maya]

fafalone said in post #1 :

So, can anyone solve for y in terms of x?

 

y^x=x^y

 

 

HI,

 

I had this small question about this problem. Here it is -

 

I was just wondering - I always thought that .....amm... it takes at least two equations to solve a two variable problem. I mean, shouldn't there be another equation like y=x or y = 5x ?

 

I thought that we can draw a graph with one equation and from there we can get the point where the curve intersects the x - axis. (Though I am not quite sure how we can draw one in this case)

 

I mean I tried this - ln(x^y) = ln(y^x) => ylnx = xlny but couldn't go further to draw a graph.

 

But I think graph is not the thing u want, right ?.

 

So, my question is - can we solve one equation with two variables? If so, how ? If the procedure is complicated u don't have to explain it - just give the name of the preocedure or better if u can post a link.

 

THANKS

 

[ PS : How did u write y^x = x^y this way - y^x=x^y ]

[Sayonara]

Use the sub and sup tags to write _subscript and ^superscript.

[neo_maya]

Sayonara³ said in post #21 :

Use the sub and sup tags to write _subscript and ^superscript.

[ THENKS A LOT ]^infinity

[Sayonara]

^That's_okay!

[Dudde]

_bleedin'^morons

[YT2095]

clifford zagnut said in post #19 :

why do you faggots keep deleting my posts? you had better get rid of your own eye dandruff before you point out my polondial cyst. i'd also like to point out that you're all a bunch of ponies galloping around someone's sick idea of... well, anyway, here's the thing: since i've got my a.s., i've lost my creativity. so my advice to all of you is to go read the a.s.o.i.

 

Dudde: And THEN SOME!!!!?

[neo_maya]

Dudde said in post #24 :

_bleedin'^morons

 

______________________________________

 

 

:flame:

 

 

:stupid:

 

 

:rant:

 

 

:down:

 

______________________________________

 

 

:jk:

 

[ I hope jk = just kidding ]

 

 

______________________________________

 

 

By the way - no no no no - BTW - How do u insert an image in a message ?