The output of tailing multiple files looks like this:
==> ./tomcat/catalina.2017-11-09.log <==
09-Nov-2017 17:53:31.496 WARNING [localhost-startStop-1] com.sun.faces.mgbean.BeanManager.addBean JSF1074
09-Nov-2017 17:53:31.496 WARNING [localhost-startStop-1] com.sun.faces.mgbean.BeanManager.addBean JSF1074
09-Nov-2017 17:53:31.496 WARNING [localhost-startStop-1] com.sun.faces.mgbean.BeanManager.addBean JSF1074
==> ./tomcat/catalina.2017-11-11.log <==
11-Nov-2017 17:53:31.496 WARNING [localhost-startStop-1] com.sun.faces.mgbean.BeanManager.addBean JSF1074
11-Nov-2017 17:53:31.496 WARNING [localhost-startStop-1] com.sun.faces.mgbean.BeanManager.addBean JSF1074
11-Nov-2017 17:53:31.496 WARNING [localhost-startStop-1] com.sun.faces.mgbean.BeanManager.addBean JSF1074
This script tracks the last filename that is printed out and puts it on the same line as the log message, then prints only messages containing "WARN" or "ERROR".