How would I find the solution, or simplify

Results 1 to 4 of 4

- Jul 31st 2012, 01:34 AM #1

- Joined
- Jul 2009
- From
- Melbourne
- Posts
- 275
- Thanks
- 4

- Jul 31st 2012, 03:28 AM #2

- Joined
- Aug 2011
- Posts
- 252
- Thanks
- 61

## Re: What is x^x^x^x...

Hi !

it is an "infinite power tower"

But your symbolism is ambiguous : it could means several different power towers. One have to use brakets to give a precise definition (in attachment)

If the tower is finite (with a finit number of x), the related function of x can be formally expressed as the first derivative of a Generalized Sophomores Dream function : Formula 12:5 in the paper "The Sophomores Dream Function"

Scribd

- Jul 31st 2012, 03:39 PM #3

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 12,028
- Thanks
- 847

## Re: What is x^x^x^x...

Hello, jgv115!

How would I find the solution, or simplify

Let

Then: .

Take logs: .

And we have: .

. . a*transcendental*equation in

We can__not__solve for

By the way, JJ is incorrect.

An exponential stack is always read "from the top down".

For example, means: .

To change the order, parentheses are required: .

- Jul 31st 2012, 11:01 PM #4

- Joined
- Aug 2011
- Posts
- 252
- Thanks
- 61

## Re: What is x^x^x^x...

Hi Soroban !

you are right about the conventional hierarchy of operations.

By the way, formal solving (for y) of the equation ln(y)-y*ln(x) is :

y = -W(-ln(x))/ln(x) where W is the Lambert function.

As others special functions, the LambertW function cannot be expressed as combination of a finite number of elementary functions.

W(x) - Wolfram|Alpha