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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.

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.

@Daniel Liu
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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?

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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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## Comments

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TopNewestBecause it is invertible, It might be possible.

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x will always remain one and it is independant of y

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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.

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I meant x=y root y

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Can u explain?

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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.

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16= 2^2^2..

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

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