from the man page
Code
--log-file=FILE
This option causes rsync to log what it is doing to a file. This is similar to the logging that a daemon does, but can be
requested for the client side and/or the server side of a non-daemon transfer. If specified as a client option, transfer log‐
ging will be enabled with a default format of "%i %n%L". See the --log-file-format option if you wish to override this..