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x^(1/x) = a

Name: Anonymous 2006-01-06 21:55

x^(1/x) = a

find x in terms of a, K go!

Name: Anonymous 2006-01-07 1:14

ln(x^(1/x)) = ln(a)

ln(x)/x = ln(a)

ln(x) = x*ln(a)

d[ln(x)]/dx = d[x*ln(a)]/dx

1/x = ln(a)

x = 1/ln(a)

i win amirite. OGC

Name: Anonymous 2006-01-07 2:31

that transcendental equation has no analytic solution. nice try though!

Name: Anonymous 2006-01-07 7:22

FUCK OFF AND DO YOUR OWN HOMEWORK NOOB

Name: Anonymous 2006-01-07 10:29 (sage)

x^(1/x)=a
(x^(1/x))^x=a^x
x=a^x
x=a^(a^x)
x=a^(a^(a^x))
x=a^(a^(a^(a^x)))
infinite loop, OH SHI-

Name: Anonymous 2006-01-07 12:39

>>2
Congrats and wow, I didn't think any of you retards would get it. You are all monotonous drones who don't truly understand the nature of the equation you utilise. Nice thinking.

Your reward is 1 free 4chan. Enjoy!

Name: Anonymous 2006-01-07 12:56

actually you got it wrong

Name: Anonymous 2006-01-07 12:56

bullshit! you can't just derive like that!

Name: Anonymous 2006-01-07 13:24 (sage)

Yes you can, just fill it in:
(1/ln(a))^(1/(1/ln(a)))=a
(1/ln(a))^(ln(a))=a
ln(a)^(-ln(a))=a
Which is obviously true.

Name: Anonymous 2006-01-07 14:51

taking a=1 instantly disproves the x=1/log(a) hypothesis.

Name: Anonymous 2006-01-07 14:58

>>9
you're making me horny

Name: Anonymous 2006-01-07 15:19

>>11
Cool. Wanna get together?

Name: Anonymous 2006-01-07 15:33

>>4 wow, that's actually the correct answer... dumb fags

Name: Anonymous 2006-01-07 16:09

>>6
I got it wrong, retard. a is a variable.

Name: Anonymous 2006-01-07 20:20

fucking americans dont know math for shit no wonder your the fattest AND stupidest country in the world

Name: Anonymous 2006-01-07 23:05

SOMEONE GET A PROFESSOR

Name: Anonymous 2006-01-08 2:56

SOMEONE GET THIS THREAD A TROLL SWEEP

WOOP WOOP WOOP WOOP WOOP!

Name: Anonymous 2006-01-08 16:13

pls answer pls

Name: Anonymous 2006-01-09 3:12

there is no answer

Name: Anonymous 2006-01-09 3:34

there should be an answer. it makes a graph doesn't it? rotate it 90degrees and you have x=..

Name: Anonymous 2006-01-09 4:54

no. it's not solvable.

Name: Anonymous 2006-01-09 9:35

-[LambertW(-ln(a))]/ln(a)

Name: Anonymous 2006-01-09 11:12

elementary functions, even heard of them, you fruitcake? that's not a valid, closed-form solution.

Name: Anonymous 2006-01-09 11:53

let "1" + "1" = "2".
now find "2" in terms of "1".

Name: Anonymous 2006-01-09 12:46

>>23

Define an elementary function.

Name: Anonymous 2006-01-09 13:55

>>25

polynomials, trigonometric functions, hyperbolic functions, logarithmic functions, exponential functions, n-th root functions, and their FINITE, CLOSED-FORM combinations.

for instance, erf(x) and zeta(x) do not qualify.

Name: Anonymous 2006-01-09 17:57

The solution was already posted by >>4. Anyone posting after that is a fucking idiot.

Name: Anonymous 2006-01-09 19:48 (sage)

>>27

Especially you, for not knowing that 4channers don't care.

Name: Anonymous 2006-01-09 20:39

>>9

"obviously" lol, prove it fag.

Name: Anonymous 2006-01-10 11:50 (sage)

>>28
YOU JUST GOT OWNED AHAHAHAHAHAHAHAHAH FGT

Name: Anonymous 2006-01-10 16:31

needs more equations

Name: Anonymous 2006-01-11 5:41 (sage)

>>31
give a parametric solution then

Name: Anonymous 2006-01-11 15:15

>>32
y = x^(1/x)
http://en.wikipedia.org/wiki/Parametric

u do the rest

Name: Anonymous 2006-01-12 10:18

>>33
failt for learning math from wiki lol

Name: Anonymous 2006-01-22 16:50

>>2

Actually that's false. You can't derive an equation like this it's meaningless.

>>3
He's right.

Name: Anonymous 2006-01-23 20:55

make a proof

Name: Anonymous 2006-01-24 5:05 (sage)

even if I do a proof you won't understand it because you haven't mastered ZF, FOL or elementary analysis.

Name: Anonymous 2006-01-24 15:45

>>37
If you can't make a proof after spending 3 years studying maths in college or whatever it means you are stupid and inferior.

Name: Anonymous 2006-01-25 8:50

This equation doesn't have a definite solution without YOF or RV

Name: Anonymous 2006-01-25 12:34

>>38
I said that you're too dumb to understand it, not that I can't do it.

Name: Anonymous 2006-01-25 13:25

>>40
You are even too stupid to realise the burden of proof is on you.

I didn't do maths in college, I have an A in A-level human biology, a B in chemistry and a B in English literature. I don't know the basic of maths, but this isn't because I'm stupid, but because I'm not omnipotent and haven't been taught maths past what I need to know for A-level chemistry. Now provide a proof.

Name: Anonymous 2006-01-25 13:26

>>40
I would also like to metnion you are inferior for not realising this.

Name: Anonymous 2006-01-25 17:13

>>41
>>42
Relax buddy. All that stress ain't good for yer heart.

Proof by contradiction:
blah blah blah
QED.

Since you don't know enough maths, then it's all the same to you anyway.

Name: Anonymous 2006-01-25 17:40

fuck, at least provide a link to it you fag

Name: Anonymous 2006-01-25 20:16

>>43
I see no proof.

Name: Anonymous 2006-01-26 1:39

Assume f(x)=x^(1/x). We are looking for it's inverse g(x)=f^-1(x) that can be expressed with a finite combination of the field operations (addition, multiplication, multiplicative inverse, addative inverse). We restrict ourselves to the rational numbers; since the rational numbers are closed under these operations it means that for each value of g(x), the argument of f(x) should be rational. However, taking g(2) we get 2=x^(1/x), for which no rational solution exists. We have a contradiction, which completes the proof.

Name: Anonymous 2006-01-27 2:00 (sage)

>>46
*clap clap clap* good sir, you have sucessfully ended this thread.

Name: Anonymous 2006-02-02 18:29

taking g(2) we get 2=x^(1/x)

how??

Name: Anonymous 2006-02-04 3:14 (sage)

>>48

The root of 2 is irrational (2^(1/2)). It's usually the first proof you learn when using contradiction and is accepted without having to state the proof over...unless of course you're a noob.

Name: Anonymous 2006-02-04 16:45

>>46
Wrong. Chaos theory implies otherwise. Let's take an ordinary equation.

Y = X^2

According to chaos theory you can find X in terms of Y. According to your theory this cannot be done.

X = Y^0.5

Now take a look at this equation, if you can't understand it you are an idiot and should gb2 high school as this thread is getting too complex for you.

sthliuashrituawrotguarwhliuahwzriuw\hr;liu\zwh\hul;wet=laweiGOTUIqwyoteiu\wyteojiWUHOTEIUq\3tkia\uh4wt

Name: Anonymous 2006-02-06 3:25

>>50
/r/ ban for stupid.

Name: Anonymous 2006-02-06 14:55

>>51
Seconded.

Name: Anonymous 2006-02-06 21:07

>>51
/r/ ban for refusing to provide proof

Name: Anonymous 2006-02-07 8:12

These hard math threads are troll heaven

Name: Anonymous 2006-02-07 14:50

>>54
The thing is they're not trolling, they just like to sit and jerk off at how smrt they are, when not everyone goes to college and does a course in Riemann geometry. It is sort of like taking 2 people, whisperring to one that sin(118^7)*65 in radians is 0.58407, then asking them the question and then going AHAHAHAH U R DUMB LOL when the one who wasn't told the answer says he can't do such an equation using mental arithmetic.

Name: Anonymous 2006-02-07 14:51

sin((118^7)*65)

Name: zeppy 2006-02-07 16:04 (sage)

z=xy

Name: Anonymous 2006-02-08 2:18

>>55 you must be either in grade-school or stuck in the 18th century, because mental arithmetic is pretty fucking useless at higher maths these days

Name: Anonymous 2006-02-08 4:11

>>58
It was an analogy you tard.

Name: Anonymous 2006-02-08 4:46

no it wasn't. you just couldn't think of a better example because you're fucking clueless.

if you think being a math nerd is somehow wrong then why are you even here? go back to your cave, turn on the tv and glorify all the beautiful celebrities or whatever it is you do

Name: Anonymous 2006-02-08 6:38

>>60
>>59 is not >>55, stfu.

Name: Anonymous 2006-02-09 22:45

x^(1/x) = 1/0

Name: Anonymous 2006-02-11 14:22

x ^ (1 / x) is:

if x == 0: ZeroDivisionError
if x == 1: 0
if x > 1: x
if x < 0: -x - 1

Name: Anonymous 2006-02-11 18:24

so when x > 1,
c = x?

or when x < 0,
c = -x -1?

Name: Anonymous 2006-02-11 20:11 (sage)

lol

Name: Anonymous 2006-02-12 11:26

>>64
What's this "c"? We haven't been introduced. I evaluated x ^ (1 / x) .

Name: Anonymous 2006-02-12 14:47

so when x > 1,
a = x?

or when x < 0,
a = -x -1?

Name: Anonymous 2006-02-12 15:13 (sage)

>>66
1^1=0?
troll harder

Name: Anonymous 2006-02-12 16:11

>>68
anonymous^anonymous = troll harder

Name: Anonymous 2006-02-15 9:44 (sage)

lol

Name: Anonymous 2006-02-21 21:22 (sage)

>>26
so fuck finity and a closed form, open the form and your fucking mind instead of limiting yourself because you cant understand it.
STRIVE

Name: Anonymous 2008-06-29 4:10

bump

Name: Anonymous 2008-07-01 17:12

>>46


but then again take e^x = a.

We can express x in terms of a using elementary functions only.

But it's not rational for any rational value other than 0.

You're proof shows that the inverse is not a finite polynomial with rational co-efficients, but I think that's all.

Name: Anonymous 2008-07-02 19:05

>>37
fuck analysis, fuck it straight in the ass

Name: Anonymous 2008-07-03 2:31

fuck it orthogonally

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