The half life of synthroid is a week. That means if you take X amount of synthyroid only one day one. By the end of the week, you will have half of that amount of synthroid, that's 1/2 X left. By the end of the second week, you'll have half of what you have the previous week, so, that'll be 1/4 X. The third week, 1/8. The fourth week, 1/16, so on and so forth.
Someone with more knowledge will have a better answer, but I think it has something to do with how quickly it leaves your body. I may be way off here!