Error Message while executing command in Arbiter for log rotation
As per MongoDB BOL Here Rotate the log file by issuing the logRotate command from the admin database in a mongo shell:

db.adminCommand( { logRotate : 1 } )


You must issue the logRotate command against the admin database in the form:

{ logRotate: 1 }


Note : Your mongod instance needs to be running with the --logpath [file] option.