/sci/ - Science & Math » Thread #10880195

129KiB, 807x935, e61.png

View Same Google iqdb SauceNAO

Show your work

Anonymous Sun 11 Aug 16:58:06 2019 No.10880195 View Reply Original Report

Quoted By: >>10880294 >>10880307

Solve for x $\epsilon \mathbb{R}$

$x^{\scriptscriptstyle x^{x^{x^{x^{x^{x^{x^{x^{...}}}}}}}}}$ = 2

Anonymous

Anonymous Sun 11 Aug 2019 17:25:14 No.10880247 Report

Quoted By: >>10880275

First, some definitions.
$u_0\left(x\right) \;=\; 0$
$\forall n \;\in\; \mathbf N,\; u_{n \,+\, 1}\left(x\right) \;=\; x^{ u_n\left(x\right) }$
$u\left(x\right) \;=\; \lim_{n \;\to\; \infty} u_n\left(x\right)$
Let $n \;\in\; \mathbf N$ .
$\ln\,u_{n \,+\, 1}\left(x\right) \;=\; u_n\left(x\right)\, \ln\,x$
Taking limit as $n\;\to\; \infty$ ,
$\ln\,u\left(x\right) \;=\; u\left(x\right)\, \ln\,x$
$u\left(x\right) \;=\; 2 \qquad\text{iff}\qquad \ln\,2 \;=\; 2\, \ln\,x \qquad\text{iff}\qquad x \;=\; \mathrm e^{ \frac{\ln\,2}2 }$

This has been brought to you by TotallyNotHomeworkThreadSolver. All rights reserved.

Anonymous

Anonymous Sun 11 Aug 2019 17:38:34 No.10880265 Report

Quoted By: >>10880298

x = sqrt(2)

proof:
just look at it, trivial

Anonymous

Anonymous Sun 11 Aug 2019 17:43:28 No.10880275 Report

Quoted By:

>>10880247
That seems like a needlessly complicated way of solving it.

$x^{x^{x^{x^{x^{x^{x^{...}}}}}}} = 2$
$x^{2} = 2$
$x = \sqrt{2}$

Anonymous

Anonymous Sun 11 Aug 2019 17:56:53 No.10880294 Report

Quoted By:

>>10880195
doesn't equal 2 ever

it diverges for x>1
diverges to 0 for x<1, x>0
diverges to 1 for x=1
undefined for x<=0

Anonymous

Anonymous Sun 11 Aug 2019 17:59:11 No.10880298 Report

Quoted By:

>>10880265
Thread

Anonymous

Anonymous Sun 11 Aug 2019 18:04:36 No.10880307 Report

Quoted By:

>>10880195
x = root(2)

Source: The thread you made on this last week

Anonymous

Anonymous Sun 11 Aug 2019 18:22:54 No.10880348 Report

Quoted By:

Only real niggas can solve this one:
$x^{x^{x^{x^{...}}}} = 3$

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches