My answer is it depends upon you and our communication. I can produce new website designs as quickly as 24 hours but no longer than 1 week. Changes I make within 24-48 hours. Websites usually on average take 6-8 weeks, however I have build then in as little as 1 week before. For logo design, I would allow 1-3 weeks for the process.
Usually it will takes 1-3 drafts before agreeing on a suitable design for your project.
For logos especially you want to make sure you love it because you have to live with it for a long time so don't rush the process.