open( my $log_file_handle, 'logfile.log' ) or die( "Could not open fil
+e\n" );
while( <$log_file_handle> ) { 

      my $single_line_in_log_file = $_ ;

      ## Now we are dealing with only one line ... 

}

close( $log_file_handle );
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You might also want to save the line number you have reached and seek it so you can continue from where you left off, in case the program dies.