That depends. If it was completely powered off (as opposed to in sleep mode) then no that definitely isn't normal (my old Kobo Wifi and Originals can survive multiple months with little or no change in charge level when powered off). Lots of people seem to be able to read over that much time if they don't use wifi and power it off when not using it before needing to recharge. In sleep mode it is using a tiny amount of power (to keep it ready to restart) all the time, but if it was fully charged then I don't think it should have depleted completely in 3 weeks, but if you were less than fully charged it could have.
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