Is seek and tell significantly faster than simply walking through the file with a while loop until I get to where I need to be?

Uhm, yes. For the same reason that it's faster to do:

    my $element = $array [$big_num];
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than to do:

    my ($element) = grep {$_ == $big_num} 0 .. $#array;
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With a seek, you do a simple operation once. With a line-by-line scan, you do a complex operation many, many times.

Personally, I'd have the webserver log to a database.

Abigail