#Roots with tetrartion and pentation

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sour martenBOT
faint rampart
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I don't know of any way to compute the inverses of tetration or pentation like there are methods for computing logarithms and roots, but the wikipedia article seems to have a lot of information on them. https://en.wikipedia.org/wiki/Tetration#Inverse_operations

Tetration

In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though

    ↑↑
  

{\displaystyle \uparrow \uparrow }

and the left-exponent xb are common.
Under the definition as repeated exponentiation,

...

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If you're interested in these higher order operations, you might be interested in this video. https://www.youtube.com/watch?v=ofy2Kw2sIZg

YouTube
Epic Math Time
The Missing Operation | Epic Math Time

Why isn't exponentiation commutative? Or associative? Is exponentiation really the next operation after multiplication? Join me in this exploration of binary operations and ring theory.

#mathematics #math #ringtheory #abstractalgebra #epicmathtime

Special thanks to my Patreon supporters: Dru Vitale, RYAN KUEMPER, AlkanKondo89, John Patterson, ...

▶ Play video
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this video presents an alternative to tetration that is much more satisfying.

tribal lodge
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I suppose an inverse to tetration would be to do x to the power of 1/(2 to the power of n ) with n being the number of times you square a number.

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e.g 3 tetrated 3 times is 6561, 2 to the power of 3 is 8 and fittingly, the 8th root of 6561 is 3. Also 2 tetrated twice is 16. 2 to the power of 2 is four and the 4th root of 16 is 2.

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Assuming pentation is to the power of 5, same thing but replace 2 with 5.

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Ok so tetration is squaring the result of a squaring however many times yes

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for example ((2x2)(2x2))(16)

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(I can't do powers on my keyboard)

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Alright so then the root increases exponentially

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The first time you tetrate it's (xx)(xx)

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the second time is (xx)(xx)(xx)(xx)

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and the third time is (xx)(xx)(xx)(xx)(xx)(xx)(xx)(xx)

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so to reverse it simply do whatever number your using's root of 2 to the power of however many times you multiplied x by x

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5 ^ 7

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well in maths you express a root as a power by doing x^1/root

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What I want to know is do you understand why it works

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because if you do then you'll have no problem using and applying it

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Thanks

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I appreciate your effort