Calculate x when n = x^x

Asked Dec 01 '17 at 20:05

Active Dec 01 '17 at 20:18

Viewed 85 times

Is it possible when you know some n calculate the x if

$$n = x^x$$

Sorry, I did't even know how this equation is called, any help appreciate.

edited Dec 01 '17 at 20:18

asked Dec 01 '17 at 20:05

webdeb

and what is $n$ supposed to be ? – Dr. Sonnhard Graubner Dec 01 '17 at 20:06
1

Lambert W function is helpful. – Donald Splutterwit Dec 01 '17 at 20:07
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n can be any number as input, the output need to be x – webdeb Dec 01 '17 at 20:07
just use newton method – lion Dec 01 '17 at 20:08
@lion sry, what is the newton method? – webdeb Dec 01 '17 at 20:08
google Newton–Raphson method – lion Dec 01 '17 at 20:10
Also: https://math.stackexchange.com/questions/54210/is-xx-y-solvable-for-x, https://math.stackexchange.com/questions/532336/how-to-solve-equations-of-this-form-xx-n – all found with Approach0 – Martin R Dec 01 '17 at 20:11
I think this is a duplicate, of the mentioned post by @MartinR Thanks, I'll look into it! – webdeb Dec 01 '17 at 20:12
Check here: https://en.wikipedia.org/wiki/Lambert_W_function#Example_2 – John Dec 01 '17 at 20:12
Thanks guys, you are awesome :) – webdeb Dec 01 '17 at 20:12
https://math.meta.stackexchange.com/questions/27392/whats-the-deal-with-lambert-w-function-questions lol – Dec 01 '17 at 20:16
\begin{eqnarray} n= x^x \ x \ln x =e^{\ln x} \ln x = \ln n \ \ln x =W(\ln n) \ x=e^{W(\ln n)} \end{eqnarray} Where $W$ is the Lambert function https://en.wikipedia.org/wiki/Lambert_W_function – Donald Splutterwit Dec 01 '17 at 20:18
Absurd. This is wrong question – NEW SUN May 12 '18 at 14:50

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