Use the SPOOL command to direct RMAN output to a log file.
Execute the SPOOL command at the RMAN prompt.

Example 2-142 Spooling RMAN Output to a File
This example directs RMAN output to standard output for configuration of the default device type, spools output of the SHOW command to log file current_config.log, and then spools output to db_backup.log for the whole database backup:
CONFIGURE DEFAULT DEVICE TYPE TO sbt; SPOOL LOG TO '/tmp/current_config.log'; SHOW ALL; SPOOL LOG OFF; SPOOL LOG TO '/tmp/db_backup.log'; BACKUP DATABASE; SPOOL LOG OFF;