my $randomNum = getMyRandomNum();  
my $directory = "/path/to/some/dir";
openddir DIR, $directory or die "opening $directory failed";

my $specialRegex = qr/$randomNum.*log$/i;
my @logfiles = grep /$specialRegex/, readdir DIR;

for my $logfile (@logfiles) {
  open LOG "<", $logfile or warn "....";
  while (<LOG>) {
    print if dateMatches() .. 0; # should print all lines from where dateMatches() returns TRUE.
    ...
  }
}