I'm going to have to add my name to those who don't understand why this isn't a standard option, why it is that Logitech recommends that we toss the keyboard once the battery wears down? The justification some people here surmise is that it's because lithium batteries require special disposal. But what does Logitech think most people are going to have to do with the keyboards with the dead lithium batteries in them? It's irresponsible of Logitech to have this on the market and not to offer a way of replacing the battery or at the very least encouraging customers to responsibly change the battery.
Kudos to ifixit for providing responsible solutions.