Appeals to logos are arguments that are meant to persuade through logic. This is in contrast to those arguments taht appeal to pathos, trying to win emotional sympathy. In this essay by Prose, there are many places in which she tries to win us over with logic and reasoned argument.
One example of this is where Prose gathers the reading lists from some eighty or so high schools around the country. She notes which works are read most often, thus providing factual data to support her contention about what sorts of things high school students are reading.
Another example of this comes when Prose tells us about the purpose for which literature is being taught. She cites, for example, the San Francisco Board of Education's requirement that literature be taught in a way that will reflect the diversity of the community. By telling us this, she lays the basis for her argument that literature is being taught in the wrong way and that this sort of teaching is turning students off to serious literature.