Why does the natural log of number 2 show up so often??

[Kharakov]

I'm thinking it's because 2 is the most common prime, but maybe it's because it's the natural log of number 2.

 

[beero1000]

Because 2 is the next whole number after 1.

 

[Kharakov]

Because 2 is the next whole number after 1.

Well, yeah.

You have the alternating harmonic series.

Every alternating reciprocal simplex series has log(2) in it.

It pops up elsewhere:

For limit n-->infinity x=x^n-1 (positive real root, so x^n ~2) k-->infinity nestings
\(\sqrt{log(2)}= \lim_{n\to\infty} \,\, \sqrt{\left(nx^{n-1}\right)^k \,\, \times \,\, \left(x-\sqrt[n]{1+\sqrt[n]{1+\sqrt[n]{1+\dots}}} \right)}\)

if you set n=2, and x=x^2-2 (positive real root)
\(\frac{\pi}{2}= \,\, \sqrt{(4)^{k} \,\, \times \,\, \left(2-\sqrt{2+\sqrt{2+\sqrt{2+\dots}}} \right)}\)

There has to be an explanation as to why pi/2 pops up after the square root of the natural log of number 2 when using infinitely nested radicals to calculate both. Infinitely nested radicals... lemme see. Natural log of #2 is all evil, so the root of all evil is an infinitely nested radical equation... who is the infinitely nested radical?


And my computer is rooted... love the shady people... sooooo much.

 

[Bomb#20]

if you set n=2, and x=x^2-2 (positive real root)
\(\frac{\pi}{2}= \,\, \sqrt{(4)^{k} \,\, \times \,\, \left(2-\sqrt{2+\sqrt{2+\sqrt{2+\dots}}} \right)}\)

There has to be an explanation as to why pi/2 pops up after the square root of the natural log of number 2 when using infinitely nested radicals to calculate both. Infinitely nested radicals... lemme see. Natural log of #2 is all evil, so the root of all evil is an infinitely nested radical equation... who is the infinitely nested radical?

Well, since k is unidentified, it's presumably this guy:

 

[Malintent]

It's because two is the loneliest number since the number one.

 

[Kharakov]

if you set n=2, and x=x^2-2 (positive real root)
\(\frac{\pi}{2}= \,\, \sqrt{(4)^{k} \,\, \times \,\, \left(2-\sqrt{2+\sqrt{2+\sqrt{2+\dots}}} \right)}\)

There has to be an explanation as to why pi/2 pops up after the square root of the natural log of number 2 when using infinitely nested radicals to calculate both. Infinitely nested radicals... lemme see. Natural log of #2 is all evil, so the root of all evil is an infinitely nested radical equation... who is the infinitely nested radical?

Well, since k is unidentified, it's presumably this guy:

"k--> infinity nestings.... I thought it would be perfectly clear that the pi formula and the natural log of number 2 one were connected." Agent m'K ultra.

 

[Kharakov]

It's because two is the loneliest number since the number one.

Zero is the numbest number.

 

[steve_bank]

google logarithms and exponential equation solutions. Base 2 and base e exponentials are common in engineering.

 

[steve_bank]

Because 2 is the next whole number after 1.

And they say math is a humorless endeavor.