Just had an dental X-ray a month or so ago and teeth looked perfect. Now I'm noticing a little tiny brown spot at the base of my back molar. Cavity?

Different view. X-rays allow dentists to see between teeth. The location you're describing is better diagnosed with direct visual examination. Best to have your dentist take a look and treat whatever is causing the "spot.".
Possible. It would be best to see your dentist if you are concerned about this spot. While your xrays were normal, it is possible that they didn't see the small defect. It may be wear in the enamel.
Stain ? The brown spots can and may be stain from food, drink or medication on the rough enamel of the molars teeth. You should see your dentist just to be sure, plus it will put your mind at ease.