Should not have a problem. (Obviously you can wrap this in a class.)

use strict;
use warnings;

open_log();
a();
b();
close_log();

sub a {
    logging("Entering a\n");
    logging("Entering a\n");
}

sub b {
    logging("Entering b\n");
    logging("Entering b\n");
}

sub logging {
    print LOG shift;
}

sub open_log {
    open(LOG, ">", "log");
}

sub close_log {
    close LOG;
}
[download]

This gave me:

Entering a
Entering a
Entering b
Entering b
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