hi dan.
I don't know your history and whether you have suffered back pain previously and /or how much exercise you do..
basically if you haven't exercised much and then go out on a 10km paddle you could reasonably expect to get a stiff/sore back (and arms,shoulders,legs etc). that kind of muscle stiffness will go away in a day or 2 or 3
however if you're otherwise reasonably fit and active and are only getting localised pain in your lower back then it's either your posture, your technique or an underlying injury being aggravated.
As simon mentioned 'old age' could also be the problem, but theres plenty of older guys on this forum who are all paddling longish distances with no problems - no doubt due to paddle fitness they have built up over time.
I've had a crook lower back since a skiing accident in my early 20's and have been a regular visitor to chiro's, physios etc over the last 10 years. However I do note that my back only gets sore when I have been inactive and/or have put on some pudding round the guts.
After temporary relief from physio and chiro treatments aliong with their advice to 'do some strengthening exercises (BORING!!) I enrolled in a pilates class. To my surprise this was the best 'remedy" I have ever done, basically exercises to strengthen core / abdominal muscles. Every physio and chiro has told me that in order to have a strong back, first you need strong core muscles.
Hence this was part of the reason that I got my yak - for fitness /core strength and flexibilty which is a much more fun way of doing exercise than going to a gym or goingf to a pilates class. I'm just not into that scene and would much rather be doing a sport I enjoy and getting exercise while doing it
good luck with it...