my $log;   ## Oops! Need this line, so $log is scoped beyond the {}
my $LOGTIME = ...
my @emails  = qw(brother@elwood.com sister@elwood.com);
my $LOGFILE = "/home/admin/logs/check_jvm/check_jvm_$LOGTIME.log";
open(LOG,"$LOGFILE") or die;
{ undef $/;
  $log = <LOG>;
}
close LOG;

if (open(SENDMAIL, "|/usr/lib/sendmail -oi -t -odq")) {
   print SENDMAIL   "From: PROD\@elwood.com\n"
                  . "To: " . join(" ", @emails) . "\n"
                  . "Subject: Web Server Issue\n"
                  . "$log\n";
   close(SENDMAIL);
}