Running ActiveMQ as non-root with a handy script and a small tweak in conf/log4j.properties
: replace log4j.appender.logfile.file=${activemq.base}/data/activemq.log
with log4j.appender.logfile.file=${activemq.data}/activemq.log
to prevent ActiveMQ from putting the log in the installation folder.
Though I suppose you could also create a new broker instance.