Mariadb default logs location & --log-error
Going off the documentation, the error log should be in the default location of /var/lib/mysql and it should be named the default hostname.err, but it's just not there. 

In the directory /var/lib/mysql I do have a tc.log, iblogfile0, iblogfile1, aria_log.00000001, and aria_log_control files. But I cannot read any of them, they are encrypted. Anyone know what these are?


  BUT, I am starting the service using service mysqld start command so I want to know what all options are used by default when we start the service using service mysql start? ESP, is --log-error used?


After running the following command,  

cat /etc/systemd/system/mysqld.service | grep "mysql"

we can see that the line that systemd uses to start the process is ExecStart=/usr/sbin/mysqld $MYSQLD_OPTS $_WSREP_NEW_CLUSTER $_WSREP_START_POSITION. The options passed to MariaDB are stored in the $MYSQLD_OPTS variable.  

If we also run cat /etc/systemd/system/mysqld.service | grep "MYSQLD_OPTS" we get the following.  

MYSQLD_OPTS here is for users to set in /etc/systemd/system/mariadb.service.d/MY_SPECIAL.conf
Use the [Service] section and Environment="MYSQLD_OPTS=...".
ExecStart=/usr/sbin/mysqld $MYSQLD_OPTS $_WSREP_NEW_CLUSTER $_WSREP_START_POSITION


The file MY_SPECIAL.conf does not exist on my machine, as find / -name "*MY_SPECIAL*" reveals.  

I do have entries for mysqld in journalctl. So I'm thinking that it uses the the systemd system logs by default for us systemd users.  

On the MariaDB Knowledge base page for the error-log there is a paragraph that states. 


  systemd has its own logging system, and Linux distributions running systemd may log errors there instead. To view the systemd logs, use journalctl -u mariadb.


This answers the question because --log-error would be an option that could be added to MY_SPECIAL.conf file and journalctl is where mariadb logs errors by default on a systemd system.