you get a faster trace in illustrator as you downsample, because this action results in a less complex image to analyze.
and yes, you should be concerned about the resolution, as it is the most important factor with this. but have no fear!
here’s what you get if you bring an image into Illustrator at the highest resolution possible:

so here’s how you can use live trace in illustrator:
1. select the placed image, and click the live trace button in the control palette to trace it; choose black and white logo. (make sure that preview is checked in the live trace options dialog box)

after you select the black and white logo option, you will see your logo in black and white, so everything’s ok! don’t delete anything!
2. if u see there just not enough details, we have to put more threshold or select the live trace options icon from the control palette. the standard threshold value is 160. you might want to increase (or decrease) this value…

3. in the adjustments box, select resample. and use the slider to quickly adjust the image resolution, or type in the image resolution desired. then view the results in your layout:

4. now… just click on the expand button and the vector is ready:

5. now you just have to give back the colours to your logo. do this simply by using the colour codes (cmyk, rgb or pantone depending on what you need the logo for) or by using the eyedropper tool (i’m not going to offend you and explain how to do this. but if you need help, please post a comment!
and your done with live trace. isn’t that great? you have a logo for you to use in any layout you want! HA!
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