Redirect print stream from other class method

Say I have a Parent and a Child classes. I can modify only Child class.

Parent class has some print's in it.

package Parent;

use strict;
use warnings;

sub new
{
    my $class = shift;
    my $self = {};
    bless $self, $class;
    return $self;
}

sub sayHello{
    my $self = shift;
    print "Hello world\n";
}

sub sayBye{
    my $self = shift;
    print "Bye world\n";
}

1;

In my Child class I have a method to print content into log files.

package Child;

use strict;
use warnings;

use parent 'Parent';

sub new
{
    my $class = shift;
    my $self = $class->SUPER::new();
    return $self;
}

sub talk{
    my $self = shift;
    $self->sayHello;
    $self->sayBye;
}

sub talkToLog{
    my $self = shift;

    my $logName = 'file.log';

    $self->log($logName, $self->sayHello); # Here's my best (not working) try
    $self->log($logName, $self->sayBye);
}

sub log{
    my $self = shift;
    my $filename = shift;
    my $string = shift;
    open(my $fh, ">>", $filename) || die "Couldn't open file $filename: $!";
    print $fh $string;
    close $fh;
    return;
}

1;

Question: Is there some way to "catch" the stream of those prints from Child class and log that content using the log method?

Here is the pl file I'm using to try.

#!/usr/bin/perl

use strict;
use warnings;

use Child;
my $child = Child->new;

$child->talk;
$child->talkToLog;

It prints this in console:

Hello world
Bye world
Hello world
Bye world