At my company, we've probably paid anywhere from $75 to a couple thousand dollars for a logo, and you could pay more. If this is something like a publishing company logo that you'll put on your title page, and your friend isn't a well-known illustrator, I'd put it at the low end of the range.
I had a similiar situation when I was paying a friend to illustrate The Dreamcatcher Adventures, and it is kind of awkward, isn't it? What I did was figure out a price that I could afford and could possibly be profitable for me and presented that to my friend. He accepted it and was happy with it. Work together to figure out a price. An unhappy artist does not produce good work, but you are in business.