heh i hope you are kidding :) of course they log.. edit perhaps not YOUR ip address, but enough to identify users. AS number + extra data is almost as good as IP.

"When an entity or an individual is using the Quad9 infrastructure, their IP address is not logged in our system. We, however, log the geo-location of the system (city, state, country) and use this information for malicious campaign and actor analysis, as well as a component of the data we provide our threat intelligence partners. "

Not logged in 'our' system, reads to me, it is still logged somewhere. And the 'data we provide our threat intelligence partners', seems a little too vague for my likings.