Add to the configuration file in the section mysqld_safe

[mysqld_safe]
syslog

Restart your rdbms and check whether your mysqld logs to your syslog file. In the contrary remove in the starting script redirecting output and background at the executing mysqld_safe

$bindir/mysqld_safe --datadir="$datadir" --pid-file="$mysqld_pid_file_path"  $other_args # >/dev/null 2>&1 &

Do you see the following message? “Can’t log to error log and syslog at the same time. Remove all –log-error configuration options for –syslog to take effect.”
Then, check if your mysql server has some additional info about the error log with my_print_defaults

./my_print_defaults mysqld_safe safe_mysqld

When you see some value for error-log – it means there is some additional config file. Even I made the installation from the source there was an additional file in the localization /etc/my.cnf.