Tomcat normally logs using juli (java.util.logging). However it is possible to create a Tomcat that uses some other logging facility, such as log4j.
Logging at the server level (webapps do not log through this system) is not a reconfigurable option. It can only be changed by doing a custom Tomcat build, and Tomcat's logging is something that has to come up very early in the startup sequence if it is to be effective. Probably before Tomcat scans the TOMCAT_HOME/lib directory.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.
With a little knowledge, a cast iron skillet is non-stick and lasts a lifetime.