Yikes, that' abysmal. I have an iMac and use the apple wireless keyboard that comes with it and I can't even remember the last time I changed the batteries.
I may be mistaken about the battery time, so don't take my word for it. The Logitech site says about 10 days with backlight on (12 months(!) without it)[1]. And while I get the Ubuntu keyboard battery warning after 3-4 days, there still may be a few days left in it.
It's worth noting that the K810 is rechargeable, however. You can leave it plugged in over USB while it's at your desk, and unplug as needed. I carry mine around with a tablet as a laptop replacement and charge both every few days. I can handle 2 or 3 days of life if it means I don't need to stock AA batteries.
Yes, actually I like the idea of an internal chargeable battery through USB much more than replaceable AA batteries, since nowadays I´m very likely to have one (or two) USB chargers around when I´m travelling.
