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is this changing subject of formula possible? .... :X

If \(y=x^{x^{x}}\)

Make \(x\) as the subject of formula. ..

ie. \(x=f(y)\)?

Is it possible to do so ?

Note by Poonayu Sharma
3 years, 3 months ago

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I don't think it can x can be expressed by y in elemantary form, such as polynomials, trigonometry etc.In the case \(x^x=y\), the solutions for x need the Lambert W function, which is kinda weird, because it's just defined to be the solution to \(x.e^x=y\), and it cannot be expressed with elementary functions. Maybe someone who knows about it can make a note or something.In the case \(x^{x^x}\), I haven't the vaguest idea.

Bogdan Simeonov - 3 years, 3 months ago

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x will always remain one and it is independant of y

Shashwat Agarwal - 3 years, 3 months ago

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Because it is invertible, It might be possible.

Brilliant Member - 3 years, 3 months ago

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I meant x=y root y

Shashwat Agarwal - 3 years, 3 months ago

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Can u explain?

Poonayu Sharma - 3 years, 3 months ago

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the question is y=x to the power x and this continues till infity.Now if you remove 1 unit from infinity then also it remains infinity only.Hence you write y=x to the power y.

Shashwat Agarwal - 3 years, 3 months ago

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@Shashwat Agarwal It is not till infinity but only 2 consecutive powers of x and if we take an example ...

16= 2^2^2..

by ur method, we get 2=16^(1/16) 16=2^16.(in 2nd reply) ..which is incorrect

Poonayu Sharma - 3 years, 3 months ago

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@Poonayu Sharma I edited to reflect the author's intentions. Check again now.

Daniel Liu - 3 years, 3 months ago

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@Daniel Liu Are you a moderator ?

Nishant Sharma - 3 years, 3 months ago

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@Daniel Liu I didnt want the powers to go till infinity. ..but only 2 powers ..sorry to not notice your edition...but changing the subject to x with this condition, is possible?

Poonayu Sharma - 3 years, 3 months ago

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@Shashwat Agarwal If you solved it considering it going to infinity then it seems correct

Poonayu Sharma - 3 years, 3 months ago

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