Solution 1:

Very late to this discussion, but it appears that the 03catalina.policy file in both tomcat5.5 & tomcat6 doesn't actually permit writing to logfiles.

The simplest solution is to change the JULI permissions to:

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

Obviously, there may be security issues I'm not aware of, but I really can't be bothered to dig deeper - I've spent too long on this myself.

Solution 2:

A neat trick is to run the command "lsof -p PID" where PID is the process id of your tomcat server. This command will give you a list of all files opened by the process, including the log file. See Wikipedia page.

Solution 3:

By default check

/var/log/tomcat6/catalina.out 

or something like that

and check logging properties in

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

usually /usr/share/tomcat6/conf/ is symbolic link to /etc/tomcat6/

Solution 4:

They should be at CATALINA_HOME/logs

I've seen it most often at /opt/tomcat/logs, but in your case it might be /usr/share/logs