If your purpose is only to log the output of traceroute, then you should follow LameNerd's suggestion. If you need also to parse the logged output, then using Net::Traceroute is a simpler solution. It is currently implemented as a parser around the system traceroute command and produces informations that can be easily accessed. For example:

#!/usr/bin/perl

use strict;
use warnings;
use Net::Traceroute;

my $tr = Net::Traceroute->new(
           host => 'www.students.cs.unibo.it',
           queries => 1);

if ($tr->found) {
  my $hops = $tr->hops;
  foreach (1..$hops) {
    printf("%02d: %-15s %d %.3f ms\n",
           $_,
           $tr->hop_query_host($_, 1),
           $tr->hop_query_stat($_, 1),
           $tr->hop_query_time($_, 1));
  }
}
[download]

Given this sample code, it should fairly easy to do whatever you want with the retrieved data.

Ciao, Valerio