It all depends on which Tomcat bundle you installed, which depends somewhat on what OS you're running Tomcat under.
Tomcat routes its primary server log to stdout. Many Tomcats redirect this stream to TOMCAT_HOME/logs/catalina.out. You can redirect stdout yourself, however, using the same mechanism that any Unix-style command would.
When it comes to destroying a civilization, gas chambers cannot hold a candle to echo chambers.