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Me and my friends are working on this website and right now I create different icons and also the websites logo. My first question is about the logo. When saving the logo I've been working on it gets pixilated while zooming in. If you look at a proffesional logo this wont occure, how can I avoid this problem?

Secound question. The icons I'll create will be in very small sizes, I will for example make smileyes. My problem is that I dont know how to resize my icon.

If the secound questions seems a bit odd and stupid dont mind it, I'm very tired and confused.

Cheers.