You keep on declaring and initializing lexical filehandles, but never use them!

my $fh= new FileHandle;
open(LOG, "<$log_file") or die "Could not open file";
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You should decide. Either the oldstyle filehandles or the lexical ones. Also it's not needed to precreate the filehandles with new FileHandle, just use

open(my $LOG, "<$log_file") or die "Could not open file";
@logmessages=<$LOG>;
close($LOG);
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and if you do not use a perl that's more than 5 (or something like that) years old you will be just fine.