Yes, we can.
HOWEVER:
Logo design is highly subjective. What you consider a ‘great’ logo is ‘boring’ or ‘old-fashioned’ for someone else.
You can test it by asking five of your good friends for their honest opinion about your logo. 😉
We often get logo design requests with a very short general briefing and no clear design directions. The result is usually multiple revisions because the client is unclear on what he/she wants.
To ensure that you don't judge our whole service because of a few logo designs, we avoid these kinds of tasks and suggest getting very clear on what you want and only using us for the brand guidelines and branding identity once the logo design is at least 80-90% finalized.
Alternatively, we recommend hiring a logo designer on Dribbble or Behance (on a project basis) specializing in a particular style that you are after.
Fun fact: Phil Knight, the founder of Nike, did not like the ‘Swoosh’ logo initially (but changed his mind later on).