Could not start mysql or MariaDB. Permissions were ok, but mysql-bin.index permission error Using MariaDB 5.5.36. Here's what I got while trying to start MariaDB:

# syslog
Dec 14 09:40:52 vps1497 mysqld_safe: Starting mysqld daemon with databases from /var/lib/mysql
Dec 14 09:40:52 vps1497 mysqld: 141214  9:40:52 [ERROR] mysqld: File '/var/log/mysql/mariadb-bin.index' not found (Errcode: 13)
Dec 14 09:40:52 vps1497 mysqld: 141214  9:40:52 [ERROR] Aborting
Dec 14 09:40:52 vps1497 mysqld: 
Dec 14 09:40:52 vps1497 mysqld: 141214  9:40:52 [Note] /usr/sbin/mysqld: Shutdown complete

# ls -alh /var/log/mysql/
-rw-rw----  1 mysql adm    9023947 Dec  8 03:01 mariadb-bin.002905
-rw-rw----  1 mysql adm       2550 Dec  7 03:01 mariadb-bin.index


Permissions seem fine, trying to start mysql with root doesn't work. Any clue?
You need to make /var/log/mysql fully owned by mysql

chown -R mysql:mysql /var/log/mysql


Then go start MariaDB

Make sure you are logged in as abuser that can start MariaDB

If not, use sudo

sudo service mysql start