You can still create a logger for your application which is not used by other processes:
use Monolog\Logger;
use Monolog\Handler\StreamHandler;
// initialize the logger
$app['mylog'] = $app->share(function($app) {
return new Logger('mylog');
});
$app['mylog']->pushHandler(new StreamHandler('/logfile/mylog.log', Logger::INFO));
$app['mylog']->addInfo('Private Log initialized');