I'd do something like this (untested):

#!/usr/bin/perl -w
use strict;

my %firstfile;

open IN_A, "<a.log" or die "$!\n";

while (<IN_A>) {
    chomp;
    $firstfile{$_}++;
}

close IN_A;

open IN_B, "<b.log" or die "$!\n";

while (<IN_B>) {
    chomp;
    print if exists($firstfile{$_});
}

close IN_B;
[download]

Cheers,
Darren :)