Not entirely sure what you mean by "log it?"
You make an entry in your log book for the flight sector you undertake, but I haven't seen a column that requires you to enter who did the take off and landing. Nevertheless there may be logbooks with a space for this type of entry.
The person who physically carries out the takeoff or landing manouever is the person who is credited with it. In airline operations the Captain is normally required to carry out at least one take off and landing every 28 days to maintain currency. For F/O's the minimum requirement is usually 3 take offs and landings within the previous 90 days. This information would be recorded on the Operations return or some similiar document.
There are situations when a PNF carries out the landing. For example during a monitored approach. Of course at that point the PNF becomes the PF, however the sector would be logged as PNF or P2 for a First officer.
In summary if your paws are responsible for carrying out the landing, then it is marked down on the statutory document as you having done it. Somebody else carrying out the landing would not satisfy any recency qualification with the exception of those required for Autoland recency, when the credit applies to both individuals.
I am astonished that you asked this question over a year ago, and somebody answered it the same day, and only now did you acknowledge the fact!