Michael,
You should probably just chmod 600 your dovecot.log file. Here's mine (debian 8): root@messagerie-secours[CHROOT][10.10.10.19] ~ # ls /var/log/dovecot.log -rw------- 1 root root 8.3M Mar 22 16:40 /var/log/dovecot.log root@messagerie-secours[CHROOT][10.10.10.19] ~ # And here are the permissions for my /var/log directory : root@messagerie-secours[CHROOT][10.10.10.19] ~ # ls -d /var/log/ drwxr-xr-x 11 root root 4.0K Mar 22 06:25 /var/log/ root@messagerie-secours[CHROOT][10.10.10.19] ~ # -- Yassine.