That's a big "it depends" question...
While it might be easy to figure out if a user is in a certain group by checking the permissions' files, you'd have to check your httpd.conf to see what kind of log format you are using. I'm positive that you can set your log to a combined format that will retain the user accessing a specific resource (by using the authuser token on the CLF (common log format)), but on my servers I only log custom access and errors.

You might want to check out the Module mod_log_config page... HTH!

#!/home/bbq/bin/perl
# Trust no1!