IANAL, but I think it's a bit of a grey area. There's a 'fair use'/'fair dealing' exception to copyright in many jurisdictions, and two of the exceptions included in this principal are often teaching and scholarship. Now, I don't know whether figuring out the answers to text book questions would count as either teaching or scholarship, but it might. There's often also a 'commentary' exception, but again, I'm not exactly sure if that applies to your example.
I think you'd want to ask yourself who you think would be the audience for your blog. Is this for you and a few friends to discuss your solutions and explore the issues raised? To me, that sounds like the text book question was merely a jumping-off point, and the real meat of your blog would be the discussion. I think that would give you a strong argument that your excerpts qualify as fair use. On the other hand, if the true purpose of your blog is to help students copy their homework answers instead of doing the work themselves, I think the questions and the original text are much more central to your blog's value, and therefore are less likely to qualify as fair use. And if the publisher feels that you are lessening the value of their product by publishing these answers, they're both more likely to go after you AND more likely to be awarded damages, if a court agrees with them.
I can't really tell whether "I'd like to document my learning" is a genuine statement or whether it's just what you think you'll say if anyone gets you in trouble for helping others to cheat. It occurs to me that unless you're studying philosophy or something else with a lot of discussion involved, no one else is likely to be interested in sharing your learning documentation. So you could document your learning just as well by keeping the work private. That makes me think you're actually trying to help others cheat. Why? Is there a profit motivation? I'd tread carefully on this ground, both morally and legally.