I fully charged my Lenovo Yoga 300's battery and the charge was down to 29% when I switched it on again after 3 days. Surely this cannot be right?

If the computer was asleep rather than shut off during that time, it's perfectly plausible that the battery would be down to 29%. If it was actually shut off, I would estimate the battery would USUALLY stoop to 90% at lowest. This is because while the computer is off, it uses a tiny amount of energy to kind of "monitor" the power button for input. Once this tiny bit of energy gets an input, it goes and starts a chain reaction of waking up the rest of the computer. Make sure you're completely powering down your computer to save battery life.