In general, our logic is subservient to our emotions. As the etymology of the word indicates, it’s our emotions that motivate us; they move us to action by establishing what we like and dislike, what we want for ourselves and others, what we value and what we find repulsive. We then apply logic according to achieve the mandates of our emotions.
Without logic, we’d function much like other animals who are guided largely by desire and aversion, but are pretty much incapable of conceiving and realizing an alternative way of life.
Without emotion, much could get done, but frankly, why?
humans are basically emotional beings who have learned to mobilize logic to satisfy our emotional needs.