I tried to search for security Log4J issues regarding ActiveMQ 5.16.2 but I could not find any information. Does ActiveMQ Version 5.16.2 has the Log4J security problems? If so what should be done to close this gap?
You might review the ActiveMQ users mailing list to stay up-to-date on the latest project activity. All official support and development activities are discussed and documented on the mailing lists. This is standard practice for all Apache projects.
There's also a "News" section of the ActiveMQ website that may have relevant information like this update regarding CVE-2021-44228.