Database log files refer to sleepycat transaction checkpointing log files (msg_svr_base/store/mboxlist). Log file build up is a symptom of database checkpointing not happening. Log file build up can also be due to stored problems.
There should be 2 or 3 log files. If there are more, it is a sign of a potentially serious problem. The message store uses a few databases for messages and quotas, and a problem with those can lead to problems for all of the mail server.
Look in the msg_svr_base/store/mboxlist directory and make sure there are only 2 or 3 files.