"service mysql start" won't accept mysql-specific options, since that's a command of the init system. You would need to pass the --log-bin
to mysqld. But you should prefer specifying that in the config file ;-)
add in the [mysqld] stanza of my.cnf
log-bin = /path/to/log
and maybe:
expire-logs-days = 14
max-binlog-size = 500M
server-id = 1
and beware that the specified file+path must be writable by the mysql user! Your example specified /binlog. The mysql user ist surely not allowed to write files in /. You may specify a relative path like log-bin=binlog
which will then create a file called binlog inside your MySQL data directory where permissions are already set up.