In my case, OS X Sierra install made copies of my httpd config files with suffix [filename]~previous. Then it disabled lots of modules in httpd.conf (which is typical for some reason after a OS X upgrade). And then Apache kept silently crashing ... totally bewildering me.
$ ps ax | grep http
[ no http was listed! ]
# tail -f /var/log/system.log
[ this showed that apache2 was attempting to restart every 10 seconds ]
[ this showed the missing log directory error ]
Somehow during OS X upgrade, it kept a vhost I had made directly in httpd.conf (not typically wise, better to put custom stuff extra directory), and that vhost had a non-standard logging folder. OS X upgrade deleted that custom logging folder (odd that it would do that actually), and so upon restart it was silently failing since the log path had become invalid for the custom vhost I had in httpd.conf
I created directories to honor that non-standard logging folder. Huzzah, within 10 seconds apache2 had restarted and normal-ness returned. I still had to enable modules again in httpd.conf, also uncomment several lines to pull in additional configurations from extra. But once web server is running, a quick browser check to see what sites were still unreachable (or being redirected) allowed those config lines to be restored.