081004 2:35:11 [ERROR] Could not use /var/log/mysql-err.log for logging (error 13). Turning logging off for the whole duration of the MySQL server process. To turn it on again: fix the cause, shutdown the MySQL server and restart it.
The above error displayed in the mysqld.log file fter adding the below line to /etc/my.cnf under [mysqld].
Before restarting mysql I created the file and applied the proper permissions by entering the commands below from the console.
touch /var/log/mysql.log; chmod 640 /var/log/mysql.log; chown mysql.mysql /var/log/mysql.log
The problem was that selinux was configured and running in enforcing mode. I set SELINUX=disabled in /etc/selinux/config and rebooted the server. When the server came back online it was now writing to the /var/log/mysql.log file with no problem.