Logging to the same file from multiple servers can get very messy. You inevitably end up with multiple servers attempting to update files simultaneously, which has a habit of causing problems such as weirdly intermingled output and locking.
Given that you're using Log4J, then you should check out JMS queue appenders:
http://logging.apache.org/log4j/2.x/manual/appenders.html#JMSQueueAppender
Using this, every server logs to a JMS queue, and you can set up a listener which logs to file on a separate server.
A reasonable alternative would be to do a little bit of Perl scripting to grab the files and merge them periodically, or on demand.
You will probably find messages which are out of step with each other. That's because each server will be buffering up log output to avoid blocking your application processes.