#!/usr/bin/perl

use strict;
use warnings;

my ($X, $Y, $n) = @ARGV;
$n ||= 20;

my $Z = $X ** $Y;

# f(z) = log z - y * log x = 0;
# f'(z) = f1(z) = 1/z

my $ylogx = $Y * log $X;

my $z = 1;
for my $i (1..$n) {
    my $fz = log($z) - $ylogx;
    my $f1z = 1 / $z;
    $z = $z - $fz / $f1z;
    my $e = abs($z - $Z);
    printf "%3d: z=%8f, e=%8f\n", $i, $z, $e;
}