First, it is not clear what you mean by logging your activity. Do you mean manually logging an activity, such as entering that you did elliptical for 30 minutes at such-and-such a time, or do you mean, just normally recording your daily activity?
For normal recording of activity, you don't even have to be near your phone. You can just occasionally sync through your phone and wi-fi to get the activity uploaded from your tracker to the Fitbit computers. For that, your phone has to be nearby with bluetooth on.
As far as phone's GPS, it only has to be on if you want to use connected-GPS to track the map and distance of an activity.
I have also read of some version of Android telling you GPS has to be on for something, maybe syncing, but I don't know much about that.
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Best AnswerOnly during specified exercise sessions (run, walk, bike), connected-GPS gives map and gets distance from GPS rather multiplying number of steps time stride length for distance.
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