One of our esx hosts had an unexpected outage...which logs do you check after this?
to see that everything is fine on your ESX?
When you say "unexpected outage" do you mean a PSOD? If so you will want to check out the vmkernel coredumps. If you mean the host powered down/off in a way that would not be considered graceful you should check the normal logs:
/var/log/vmkwarning, /var/log/vmkernel, /var/log/messages, /var/log/vmware/hostd.log.
Or just collect log-bundles from vCenter or run vm-support command from the Service Console and browse through the logs inside the archive.
VCP 3, 4
And if you have an active SnS consider also to use VMware support.