Hi

If you charge $50 per hour for graphic design and the logo took two hours then the cost of the logo is $100. If you did additional admin work (other than graphic design) then it would be $15 per plus the logo.
But I'd make sure that your client (friend

) understood that she was contracting for graphic design (at the higher rate). Being clear with your clients on what they're paying for before you start on the project/service is important to avoid misunderstanding later.