After reviewing your design brief and criteria, here is the logo I came up with. With a subtle nod to the look of the attached file's logo (the 8-pointed star burst), and a modern flair to go with it. Overall it is a very clean and very eye-catching modern icon. Let me know what you think, and if you wish to explore any other specific colors. Thank you!
Is there a way you can you can combine the three letters in one logo like yves st. Laurent? Or perhaps make the star part of the background. Can you do some with a lower case Also skincare can be one word. We would like to see a grayscale version.
Edit: the ladies in our office said it needs to be sexy. ;-)
I like the way you brought the letters together. However we like the look of "skincare" on the first logo. Can you incorporate the two together? And make the Azl a straight black instead of a gradient.
On entry 10 can you reverse the colors, make the skin care black and white and make the AZL in color. I think that is what I meant. I think that the complete black and white may be to harsh in no. 11.