1 make plausible or believable or understandable or acceptable or reasonable, make allowance(s) or excuses for, vindicate, account for, justify, excuse, reason away, explain away:
How can you rationalize taking my car without my permission?
2 think through, reason out; apply logic to, ratiocinate:
He warps the statistics to rationalize his argument. The fundamentalists make no attempt to rationalize their literal interpretation of the Scripture.