log4jdbc sends all events to SLF4J and then the underlying logger.
Depending on which type of logging system you use, and how creative
you are, you might be able to accomplish that.
For example, logback has an appender, called the "SiftingAppender"
that is designed to do just what you said:
See
http://logback.qos.ch/manual/appenders.html#SiftingAppender
However, I'm not sure if the log messages that log4jdbc produces have
enough information needed to sift the events properly.
But the design of log4jdbc is quite simple and I'm sure you could get
it done with some slight changes to log4dbc together with such an
appender.