<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def _check_existing_logger(loggername, short_name):
 """ Check if logger with name loggername exists. :param loggername: Name of logger. :param short_name: Shortened name for the logger. :return: Logger or None """

    if loggername in LOGGERS:
        # Check if short_name matches the existing one, if not update it
        if isinstance(LOGGERS[loggername], BenchLoggerAdapter):
            if ("source" not in LOGGERS[loggername].extra or
                    LOGGERS[loggername].extra["source"] != short_name):
                LOGGERS[loggername].extra["source"] = short_name
        return LOGGERS[loggername]
    return None