Each application must use its own log4j. You can achieve this by placing log4j.jar in WEB-INF/lib of each application.
In each log4j's configuration file (default location is WEB-INF/classes), specify the log file name, e.g. log4j.appender.AppLog.File=${catalina.home}/logs/app1.log.
Add swallowOutput="true" for each context so stdout, stderr will go to your own log.
We do this on Tomcat 5.5 but I think it should work on 6.0 also.