Question

Has the equation $r^x\cdot \ln(r)=\ln(x)$ for $r<e^{-e}\ \ $ $3$ solutions?

score 181 · Answer 1 · 2017-12-09 09:38:13

181

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Has the equation $r^x\cdot \ln(r)=\ln(x)$ for $r<e^{-e}\ \ $ $3$ solutions?

Published on 09 Dec 2017 - 9:38

score 203 · Answer 2 · 2026-03-26 23:11:22

203

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Does $\lim_{n\rightarrow \infty} \left(r+\frac{1}{n^2}\right)\uparrow \uparrow n=e$ hold?

Published on 26 Mar 2026 - 23:11

score 62 · Answer 3 · 2017-12-09 14:30:24

62

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How slow does the iteration $x_1=r$ , $x_{n+1}=r^{x_n}$ converge for $r=e^{-e}$?

Published on 09 Dec 2017 - 14:30

score 257 · Answer 4 · 2026-03-26 23:11:22

257

Views

Shortcut to $x\uparrow \uparrow n$ for very large $n$ and $x\approx e^{(e^{-1})}$?

Published on 26 Mar 2026 - 23:11

score 218 · Answer 5 · 2017-12-14 16:52:58

218

Views

Quickly show that $\Bigg|(-1/2)^{(-1/2)^{(-1/2)}}\Bigg|=e^{\pi\sqrt{2}}$

Published on 14 Dec 2017 - 16:52

score 183 · Answer 6 · 2026-03-26 01:23:29

183

Views

Magnitude of $f_3(n)$ compared to power towers of tens

Published on 26 Mar 2026 - 1:23

score 185 · Answer 7 · 2017-12-30 16:57:04

185

Views

General formula of first order derivative of the nth tetration of ln(x).

Published on 30 Dec 2017 - 16:57

score 185 · Answer 8 · 2017-12-30 18:47:12

185

Views

Indefinite Integral of $ \ln(x)^{\ln(x)^{\ln(x)^{.^{.^{.^{\ln(x)}}}}}}$ for an $ n $-number of $ \ln(x) $'s with respect to $ x $

Published on 30 Dec 2017 - 18:47

score 1k · Answer 9 · 2010-11-25 19:53:03

1k

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Could real iterates of the Taylor Series expansion of $b^x$ help to find a way to define tetration?

Published on 25 Nov 2010 - 19:53

score 16k · Answer 10 · 2026-03-25 18:49:46

16k

Views

Why are addition and multiplication commutative, but not exponentiation?

Published on 25 Mar 2026 - 18:49

score 550 · Answer 11 · 2011-06-25 01:22:06

550

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What is the Equivalent Form of Tetration to the Exponential $n^{1/n}$?

Published on 25 Jun 2011 - 1:22

score 7.1k · Answer 12 · 2011-08-10 06:13:24

7.1k

Views

Is There a Natural Way to Extend Repeated Exponentiation Beyond Integers?

Published on 10 Aug 2011 - 6:13

score 1.5k · Answer 13 · 2011-08-22 15:57:22

1.5k

Views

How to calculate $f(x)$ in $f(f(x)) = e^x$?

Published on 22 Aug 2011 - 15:57

score 7.2k · Answer 14 · 2011-09-19 19:28:57

7.2k

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thoughts about $f(f(x))=e^x$

Published on 19 Sep 2011 - 19:28

score 9.1k · Answer 15 · 2011-12-02 22:32:24

9.1k

Views

Are these solutions of $2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$ correct?

Published on 02 Dec 2011 - 22:32

List Question

Has the equation $r^x\cdot \ln(r)=\ln(x)$ for $r<e^{-e}\ \ $ $3$ solutions?

Does $\lim_{n\rightarrow \infty} \left(r+\frac{1}{n^2}\right)\uparrow \uparrow n=e$ hold?

How slow does the iteration $x_1=r$ , $x_{n+1}=r^{x_n}$ converge for $r=e^{-e}$?

Shortcut to $x\uparrow \uparrow n$ for very large $n$ and $x\approx e^{(e^{-1})}$?

Quickly show that $\Bigg|(-1/2)^{(-1/2)^{(-1/2)}}\Bigg|=e^{\pi\sqrt{2}}$

Magnitude of $f_3(n)$ compared to power towers of tens

General formula of first order derivative of the nth tetration of ln(x).

Indefinite Integral of $ \ln(x)^{\ln(x)^{\ln(x)^{.^{.^{.^{\ln(x)}}}}}}$ for an $ n $-number of $ \ln(x) $'s with respect to $ x $

Could real iterates of the Taylor Series expansion of $b^x$ help to find a way to define tetration?

Why are addition and multiplication commutative, but not exponentiation?

What is the Equivalent Form of Tetration to the Exponential $n^{1/n}$?

Is There a Natural Way to Extend Repeated Exponentiation Beyond Integers?

How to calculate $f(x)$ in $f(f(x)) = e^x$?

thoughts about $f(f(x))=e^x$

Are these solutions of $2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$ correct?

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