Using a "relative path" in a web application means relative to the application server's working directory. There's only one working directory for a JVM so it can't be related to any of the applications being run in the server. And that makes it useless for you.
You can put "${abc}" into a log4j configuration file and the configurator will replace that with the value of the "abc"
Java system property. But again, system properties are one-per-JVM and not one-per-webapp so that probably isn't much more helpful.
Besides, if you put the logs into the web app then when you install a new WAR or EAR file, you lose all of those logs. You might want to consider logging to a fixed location outside of the application server.