Honestly, I think you are going about this the wrong way. You really should be looking at something like File::Log

Failing that, you could do something like this:

#!/usr/bin/perl -w
use strict;
use POSIX qw(strftime);

my $start = time();

print "Started at ", (strftime "%a %b %e %H:%M:%S %Y", localtime($star
+t)), "\n";

for (1 .. 5) {
    print "Logging some stuff...\n";
    sleep 1;
}

my $end = time();

print "Ended at ", (strftime "%a %b %e %H:%M:%S %Y", localtime($end)),
+ "\n";

print "Total run time:", $end-$start, " seconds\n";
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Which when run, gives you:

Started at Thu Dec 22 14:59:20 2005
Logging some stuff...
Logging some stuff...
Logging some stuff...
Logging some stuff...
Logging some stuff...
Ended at Thu Dec 22 14:59:25 2005
Total run time:5 seconds
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Then you simply redirect that to your logfile in the same way as you originally did.