An argument based on logic and reason rather than emotion and personal opinion is best described as
objective.
rhetorical.
biased.
weak.

Objective An argument based on logic and reason rather than emotion and personal opinion is best described as objective. This type of argument often has to do with logos, that is, reason, evidence and logic. These generally deal with material questions or things that can be sensed or measured; things that are associated with the real outside world, outside of oneself. The other choices in this question: rhetoric, biased and weak do not fit with the description that was given in the question.