Compilando MySQL

Hola experto.
Tengo nu problema al instalar MySQL. Después de hacer el configure, el make y el make install.
Al hacer /usr/local/mysql/bin/safe.mysqld &, me sale:
/usr/local/mysql/bin/safe_mysqld &
[1] 27513
[root@localhost mysql]# Starting mysqld daemon with databases from /usr/local/mysql/var
/usr/local/mysql/bin/safe_mysqld: /usr/local/mysql/var/localhost.localdomain.err: No
existe el fichero o el directorio
/usr/local/mysql/bin/safe_mysqld: /usr/local/mysql/var/localhost.localdomain.err: No
existe el fichero o el directorio
/usr/local/mysql/bin/safe_mysqld: /usr/local/mysql/var/localhost.localdomain.err: No
existe el fichero o el directorio
mysqld daemon ended
[1]+ Done /usr/local/mysql/bin/safe_mysqld
¿a que se debe el error?
He seguido, pero justo después, al hacer:
/usr/local/mysql/bin/mysqladmin -u root password miclave
me sale:
/usr/local/mysql/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/tmp/mysql.sock' (2)'
Check that mysqld is running and that the socket: '/tmp/mysql.sock' exists!
[root@localhost mysql]# /usr/local/mysql/bin/mysqladmin -u root password nuevopass
/usr/local/mysql/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/tmp/mysql.sock' (2)'
Check that mysqld is running and that the socket: '/tmp/mysql.sock' exists!
¿A qué puede deberse?
Muchas gracias. Saludos.