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 ?

#Algebra #NumberTheory #AlgebraicManipulation

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

Because it is invertible, It might be possible.

A Former Brilliant Member - 6 years, 11 months ago

x will always remain one and it is independant of y

Shashwat Agarwal - 6 years, 11 months ago

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 - 6 years, 11 months ago

I meant x=y root y

Shashwat Agarwal - 6 years, 11 months ago

Can u explain?

Poonayu Sharma - 6 years, 11 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.

Shashwat Agarwal - 6 years, 11 months ago

@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 - 6 years, 11 months ago

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

Daniel Liu - 6 years, 11 months ago

@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 - 6 years, 11 months ago

@Daniel Liu – Are you a moderator ?

Nishant Sharma - 6 years, 11 months ago

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

Poonayu Sharma - 6 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$