Hi @Zahkc, I've moved your post into the "OS" section since we're talking dev now!
unity-system-compositor's log should normally be in /var/log/lightdm/unity-system-compositor.log. You may find the accompanying lightdm.log in that folder useful depending on the error. unity8's log should be in ~/.cache/upstart/unity8.log and might have some useful information as well.