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

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

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

Is it possible to do so ?

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

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

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

Is it possible to do so ?

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TopNewestI 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 · 2 years, 8 months ago

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x will always remain one and it is independant of y – Shashwat Agarwal · 2 years, 8 months ago

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Because it is invertible, It might be possible. – Anup Navin · 2 years, 8 months ago

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I meant x=y root y – Shashwat Agarwal · 2 years, 8 months ago

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– Poonayu Sharma · 2 years, 8 months ago

Can u explain?Log in to reply

– Shashwat Agarwal · 2 years, 8 months ago

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.Log in to reply

16= 2^2^2..

by ur method, we get 2=16^(1/16) 16=2^16.(in 2nd reply) ..which is incorrect – Poonayu Sharma · 2 years, 8 months ago

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– Daniel Liu · 2 years, 8 months ago

I edited to reflect the author's intentions. Check again now.Log in to reply

– Nishant Sharma · 2 years, 8 months ago

Are you a moderator ?Log in to reply

– Poonayu Sharma · 2 years, 8 months ago

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?Log in to reply

– Poonayu Sharma · 2 years, 8 months ago

If you solved it considering it going to infinity then it seems correctLog in to reply