Do you have another machine running an ssh server? If so, you can switch to the second console by pressing Alt+F2, then install an ssh client by entering 'anna-install openssh-client-udeb', and then use scp to copy out /var/log/syslog.
Do you have another machine running an ssh server? If so, you can switch to the second console by pressing Alt+F2, then install an ssh client by entering 'anna-install openssh- client- udeb', and then use scp to copy out /var/log/syslog.