... even without the pragmas & declaration of the variable ...

cat ~/p ; rm -f log.txt ; ~/p ; cat log.txt
#!~/bin/perl5.14.1

$abc = `date`;
#$abc = "Hello";

print "DATE : $abc\n";
system("echo $abc >> log.txt");

__END__

DATE : Fri Jul 15 02:07:45 HST 2011

Fri Jul 15 02:07:45 HST 2011
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... I note just in case somebody wanted to nit pick.