Can anyone help a fellow hoster out with the location of the correct logs for the following:

-Sendmail
-Apache
-exim

My apache be crashing these days and i'm getting pissed. I suspect a spammer using my services.

in rh and freebsd, check:
sendmail - /var/log/maillog
httpd - /etc/httpd/logs (depending on install location)
exim - no idea

The location of the apache log(s) would be defined in your httpd.conf (in modern versions of Apache).

Frank