The replicator generates it's own log files. These log files are all written into their own directory within the installation directory structure. In addition, symbolic links are generated for easier access to light weight logs more suited for general user use.
For example, this is the listing of the default log directory, /opt/continuent/service_logs:
mysqldump.log -> /opt/continuent/tungsten/tungsten-replicator/log/mysqldump.log replicator-user.log -> /opt/continuent/tungsten/tungsten-replicator/log/replicator-user.log trepsvc.log -> /opt/continuent/tungsten/tungsten-replicator/log/trepsvc.log xtrabackup.log -> /opt/continuent/tungsten/tungsten-replicator/log/xtrabackup.log
As you can see, each log file is a symlink to the user-level log, and the more detailed log, along with logs for backups, if they exist.