# Tetration Forum

Full Version: Infinite towers & solutions to Lambert W-function
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The solution to the equation:
Code:
x*c^x -1 = 0
Seems to be given by:
Code:
lim n->inf (1/c)^^n
Put c=e, and you get the Lambert W-function.

x*c^x = 1
lim n->inf (1/x)^^n
The limit $x=\lim_{n\to\infty} \frac{1}{c}[4]n$ satisfies the equation
$\left(\frac{1}{c}\right)^x = x$ (if I add another $\frac{1}{c}$ at the bottom of the infinite tower, the value must stay the same).
$1=c^x x$