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.

[1] http://logitech-en-amr.custhelp.com/app/answers/detail/a_id/...