Re: [FUN] CodeGolf: solve equation x^x=C

[Albert Chan <albertmcchan@...>]

On Jun 28, 2019, at 8:37 AM, Albert Chan <albertmcchan@yahoo.com> wrote:
> x^x = c
> x ln(x) = ln(c)
> x = ln(c)/ln(x) = log(c,x)
> 
> Above iterated solution converge only if denominator ln(x) > 1
> x > e
> c = x^x > e^e ~ 15.155 < 15.5

I made a mistake about the constant 15.5
It had nothing to do with e^e, but with the initial guess of x

With initial guess of 3, and actual x<3, we have
x0 = 3, x1 = log(c,3), x2 = log(c, log(c,3)) ...
Solving x2<3, we get c > 15.21708982

Had we use a higher guess, say 4, we would have c > 16