put "swallowOutput" in your context.xml
<Context swallowOutput="true">
...
</Context>
and add an individual logging.properties file into each of your webapps/wars at the position
/WEB-INF/classes/logging.properties
You can put this file also in the source-folder if your WAR is generated, e.g. by eclipse
/src/logging.properties
The logging.properties may have the following contents
handlers = org.apache.juli.FileHandler, java.util.logging.ConsoleHandler
############################################################
# Handler specific properties.
# Describes specific configuration info for Handlers.
############################################################
org.apache.juli.FileHandler.level = FINE
org.apache.juli.FileHandler.directory = ${catalina.base}/logs
org.apache.juli.FileHandler.prefix = webapp_name.
java.util.logging.ConsoleHandler.level = FINE
java.util.logging.ConsoleHandler.formatter = java.util.logging.OneLineFormatter
and you can define the name prefix for each individual webapp log with org.apache.juli.FileHandler.prefix