The three elements of persuasive appeals are identified by Aristotle in his discussion of rhetoric. The first element is ethos, and it establishes the credibility of the speaker or writer and lets the audience know that he or she is trustworthy and ethical and can, therefore, safely be believed. When a company hires a celebrity spokesperson—say, an athlete to promote running shoes—it is using ethos to appeal to its customers. Also, when a speaker presents his or her qualifications for talking about a particular topic, this is is an appeal to ethos.
The second element is pathos, the appeal to emotions. A speaker or writer tries to persuade the audience by making them feel a certain way. A company might, for instance, show a set of thrilling scenes surrounding a particular car to make potential buyers excited and interested in all the fun they could have if they bought the vehicle. Further, a charity might show images of hungry children to encourage people to feel sorry and donate to its cause. This is pathos in action.
The third element is logos, and it appeals to the audience's reason. It presents facts, statistics, logical arguments, and plenty of reasons and evidence to support a claim. Someone presenting a proposal for an expanded budget at work would use plenty of numbers and factual data to show logical reasons for the increase. Also, a student defending a thesis or dissertation would clearly and carefully present his or her argument, reasons, and evidence in an orderly fashion. This is logos.
The second part of this question is quite personal. Think about the kinds of products you buy and whether or not you've ever purchased anything based off a commercial. Then consider whether that commercial used ethos, pathos, logos, or a combination of them. You might also remember presentations you've heard or political advertisements or even debates with friends. Examine these for ethos, pathos, and logos, and decide if you were or were not convinced by these elements of persuasive appeal.