use strict;
use warnings;

use Data::Dumper;

open my $logFH, q{<}, \ <<'EOD' or die qq{open: << HEREDOC: $!\n};
2009-02-02 06:12:57,500 dates processed: 2009-01-31, 2009-01-29, 2009-01-30
2009-02-18 06:03:47,713 dates processed: 2009-02-16, 2009-02-17
Different line here
2009-02-19 05:58:29,138 dates processed: 2009-02-18
EOD

my @results = ();
while( <$logFH> )
{
    chomp;
    push( @results, [] ), next unless m{dates processed:};
    my @dates = m{(\d{4}-\d\d-\d\d)}g;
    push @results, \ @dates;
}

close $logFH or die qq{close: << HEREDOC: $!\n};

print Data::Dumper->Dumpxs( [ \ @results ], [ qw{ *results } ] );