you can use MDC (mapped diagnostic context) support to route logging for each tenant into a separate file/dir/whatever.
you can read up on the concept here. it exists in slf4/logback and log4j
simply put, you set some property like tenantName in the MDC at the beginning of every request processing according to the specific tenant making the request and then use this property in your logging configuration to determine the log file into which log messages are written.