Tomcat is installed with CATALINA_HOME in /usr/share/tomcat6
CATALINA_BASE in /var/lib/tomcat6,
following the rules from /usr/share/doc/tomcat6-common/RUNNING.txt.gz.

$ ps -ax
/usr/bin/jsvc -user tomcat6 -cp /usr/share/java/commons-daemon.jar:/usr/share/tomcat6/bin/bootstrap.jar -outfile SYSLOG -errfile SYSLOG -pidfile /var/run/tomcat6.pid

$  for PID in $(pgrep jsvc);do sudo ls -l /proc/$PID/fd|grep ' 1 -> ';done
l-wx------ 1 root 500 64 2010-03-30 13:29 1 -> pipe:[301470406]
lrwx------ 1 root 500 64 2010-03-30 13:29 1 -> /dev/null
l-wx------ 1 root root 64 2010-03-30 13:29 1 -> pipe:[301470406]

// These permissions apply to JULI
grant codeBase "file:${catalina.home}/bin/tomcat-juli.jar" {
    permission java.security.AllPermission;
};

/var/log/tomcat6/catalina.out

/usr/share/tomcat6/conf/logging.properties

tail -f /var/log/tomcat7/*.log /var/log/tomcat7/*.txt /var/log/tomcat7/*.out

sudo lsof | grep -E "java.*(out|txt|log)$"