After you set RMAN log location, the next problem that you want to solve is the format of timestamp in the log, which was too coarse to judge the actual time like this:
Set NLS_DATE_FORMAT for RMAN
If you are using sqlplus, you can ALTER SESSION SET NLS_DATE_FORMAT to modify the date format, but RMAN has no such command to run. As a matter of fact, it follows OS setting, so you must set NLS_DATE_FORMAT as an environment variable on OS-level for RMAN to use.
For UNIX/Linux Platforms
$ export NLS_DATE_FORMAT='yyyy/mm/dd hh24:mi:ss'
$ rman target /
For Windows Platforms
> set NLS_DATE_FORMAT=yyyy/mm/dd hh24:mi:ss
> rman target /
Please notice that, you cannot use any quotes to set the environment variable in Windows platform, otherwise, you will see errors in RMAN.
Set NLS_LANG for Export / Import
Another environment variable that you may need to set is NLS_LANG in order to notify database to set correct NLS conventions.