The rhetoric of logos is based on what it sounds like: logic. According to Aristotle it is supported by "proof, or apparent proof, provided by the words of the speech [or text] itself." It is the use of argumentation and rational appeals based on facts, case studies, statistics, anecdotes, experiments, logical reasoning, and analogies. Think of toothpaste commercials that claim "Nine out of ten dentists recommend Crust because studies show it prevents cavities."
Strong arguments should have a balance of ethos (ethical appeals), pathos (emotional appeals), and logos (rational appeals). Logic often seems like the most convincing element of an argument, but many times the listener has to depend on the ethos of the speaker in order to believe the logos of his or her argument. In other words, you have to take the writer's word for it, whatever "it" may be.
McDonald's is not immune to rational appeals. There has to be some logic in our choice to eat there. Watch this commercial and think about how McDonald's uses logos to get customers to buy their product.
How is McDonald's using logos in this commercial? Think about how food advertisers use logos to sell their products. Is the food nutritious, easy to eat, easy to clean up? What is McDonald's saying about their fast food?
If you were an advertising executive, where would you position these commercials? To what demographic would you appeal?