@dragon123: You're not providing enough information. Are you getting an error? If so, which? Did you bundle log4j with your application, or make sure that log4j is actually supported?
The actual file that you want to be logging to seems ok, i.e., that directory should be accessible and writable from a Kindlet without the Kindlet jailbreak.
Still, I think that log4j is a massive overkill for what you're trying to do. If all you want to do is output some text to a file, I suggest to simply write an extremely simple Logging utility yourself.
I'm using
this trivial peace of code in JBPatch. You could of course create something more prowerful, with logging levels etc. - but it will still be MUCH less complicated than using a full-blown logging framework like log4j.