Thanks for pointing out the broken link, it must have disappeared in the forum conversion. I can't find the link again, but the solution is to make a log rotation for the SLiM log. Here's how:
Save the code below as /etc/logrotate.d/slim
/var/log/slim.log {
compress
rotate 1
size=+1024k
notifempty
missingok
copytruncate
noolddir
}
EDIT: I found the link, and I've fixed it.