I did a simple test inserting tuples in a table during replication:
The attached file 'master_slave-db_size-6.jpg' shows that
the size of the log directory (and number of files in the log directory)
increases continuously during replication, while on master the size
(and number of files) never exceeds ~12Mb (12 files?) in this scenario.
The seg0 directory on the slave stays at the same size as the master