Use transformations to sketch a graph of y=log_2_(x-3)+2 and determine the domain and range.

I know log_2_(x) is being moved 3 units to the right and shifted 2 units upward, its just the log in there that is throwing me off how to properly graph this thing.

Also for the domain, i thing (but please correct me if im wrong) that you cant log a 0 or negative number so the domain would have to be x>3.

Thanks.