cd /var du -sh *
If the log directory is the problem:
rm -f /var/log/*.1 rm -f /var/log/*.2 rm -f /var/log/*.3 rm -f /var/log/*.4
(The /var/log directory contains archived files that always end with a number: exim_mainlog.1. Any file ending with a number can be safely deleted.)
If the problem is with the exim_mainlog being too large, try rotating the logs:
/usr/sbin/logrotate -vf /etc/logrotate.conf
If you get an error about a duplicate log entry:
cd /etc/logrotate.d rm -rf httpd.rpmorig.log
And try the rotate again.
If the problem is in spool:
cd /var/spool/exim/msglog rm -rf *