Use can use something like this:

my $logger = sub {
    $log->message(@_);
}

# now you can call $logger like this:
$logger->('This is a logging message');
# or like that:
&$logger('This is a logging message');
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Don't know if that answers your question, though.

Update: on second reading I think your problem is a different one: you want to print $log. But what do you want the output to be? An object doesn't have a nice default string representation.