Airdrop logging on a Mac Computer
You can use the mdls -raw command to view the metadata for files on your Mac.
Example: mdls -raw /pathToYourFile
If a file was sent to you via airdrop, that file will have metadata that contains "com.apple.AirDrop". All you need to do to see all files that were sent to your Mac Computer via airdrop is run the mdfind command and search for "com.apple.AirDrop".
Example: mdfind com.apple.AirDrop
You can also use the mdfind command to search in a specific directory for certain file types.
Example: mdfind -onlyin ~/Downloads/ com.apple.AirDrop | grep .jpg