Well there are a few definitions of reasonable--some closer to logic and others farther. One definition (which I'm not using) is reasonable simply means acceptable -- for example "my wife treats me reasonably well"--well, that just means one can come up with an argument which evokes a sense of feeling good about the treatment. Now here, this is reasonable in closer to the sense of Jungian feeling--that one's reason evokes a sense of acceptance/rejection, hence is subjective rather than objective.
OTOH, there's a stricter notion of reasonable, which says reason involves a truth-claim where one claims logic applies to experience in a certain way that can actually be checked. This is e.g. the claim that an equation reasonably explains the motion of an electron in certain situations. Here the difference between reason and logic does still exist, as there are many logical formulations of the roughly "same" reason, but the claim that one's explanation is reasonable does involve being able to check logic against experience. And if one cannot, one says the claim isn't reasonable: one can't reason logically about it!! One can only surmise it may be true or false, but that there's no reasonable way to check it--here "reasonable" refers to the capability of deciding the truth-value by logical means (still, again, distinguished from precise logical formulation). This is the version I was using.
But I'm happy to be involved again