i think it should be
log=mysqld.log
so it will create log file in /var/lib/mysql direcotry (redhat, centos)
how ever
make sure you gave permission mysql to write in /var/log/mysqld/mysqld.log direcotyr
go to
cd /var/log
ls -l
see mysqld direcotry is writtiable via mysql
chown -R mysql:mysql mysqld