One technique is to use select to redirect STDOUT to a different file handle. It's often convenient to use a file opened on a string:

#!/usr/bin/perl
use warnings;
use strict;

my $log;

open my $logOut, '>', \$log;
my $oldStdOut = select $logOut;

print "this goes to the log string\n";

select $oldStdOut;
close $logOut;

print "From log: $log";
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Prints:

From log: this goes to the log string
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