Well there are quite a few ways. One method would be to store the log in a hash (or an array):

my %log_file_hash = ();
my @log_file_array;
my $linenum = 0;
my $line;

open FILE, "logfile.txt";

while ($line = <FILE>)
{
  chomp $line;
  $log_file_hash{$linenum} = $line;
  push @log_file_array, $line;
  $linenum++;
}

#now the whole file is in the hash and array.
print "The first line is " . $log_file_hash{"0"} . "\n";
print "From the array... " . $log_file_array[0] . "\n";
[download]

Another way to do this is to just store the last 4 lines and sort of move a frame over your data:

$line_0 = "";
$line_1 = "";
$line_2 = "";
$line_3 = "";

while ($line = <FILE>)
{
  chomp $line;
  $line_3 = $line_2;
  $line_2 = $line_1;
  $line_1 = $line_0;
  $line_0 = $line;
}
[download]

Hopefully this is useful. If I misunderstood your question just let me know.

Update: minor inplace grammar edits.