[color=#333333]I've been asked to design logo and this is my first professional logo. What do you think I should charge? Thanks.

many factors, most major of which, which most commission artists will agree with,
Time and Effort to make.
How others perceive your works quality.
How YOU perceive your works quality.

Its only worth as much as you and others are willing to put in it.
So do a few samples, show us some of your work, and what you think you should be charging.

[color="#333333"]I've been asked to design logo and this is my first professional logo. What do you think I should charge? Thanks.

One of many rules of thumb I keep at the back of my mind when pricing is what will it cost them to do it themselves? Just make sure you charge less than that amount ;) For example, if they'd hired someone for a n-dollars-per-hour wage and also had to buy the software, then you can claim that same n-dollars-per-hour, plus some proportion to cover the overheads of buying your software and insurance and whatever - and you'd avoid the customer thinking "Man, I could just get Frank-the-Janitor's kid in to do this cheaper."