There is a difference between analyzing an argument’s appeals and identifying them. Analysis requires that you unpack these appeals, show how they work.
When analyzing ethical appeals, you need to address both the artistic and inartistic. What are the credentials the author walks in with? And then how (specifically) does the author demonstrate that s/he is fair-minded (this means toward the opposition), intelligent or knowledgeable, and trustworthy (demonstrates good will toward the audience; not trying to deceive the audience)?
When analyzing pathetic appeals, you need to address the ways that the appeals are made (typically by emotionally charged language and by vivid description), the emotions the appeals evoke (fear, anger, shame, regret, delight, etc.), and why evoking those emotions help accomplish the purpose of the argument. So you won’t want simply to identify a pathetic appeal; you will want to explain why it is a pathetic appeal and how it works.
When analyzing logical appeals, it is not sufficient to note the use of some external fact (the statement of a law, expert witness testimony, or statistic); you must, rather, make something of that external fact to encourage the audience to come to some conclusion based on it. To note that the author says “X amount of dollars were invested in X stock” or that “X% of all Y is imported” is not in itself an analysis of a logical appeal—it is the identification of external “facts.” To analyze the logical appeal, you would have to demonstrate how this external fact or statistic gets used as a logical proof; you would have to explain the process of reasoning involved in it. Is it deductive? If so, how? Is it inductive? If so, how? How does it work? Unpack it. If an enlightening enthymeme is involved, explain it—what are its major and minor premises and what is the conclusion? If historical examples are used, lay them out. If an analogy is offered, make sense of it for us. Etc. It is also not sufficient to identify the use of an example or an analogy, for example, as a logical appeal; you’ll also need to analyze how it’s working as such. What sort of reasoning is the analogy provoking? I might say “the author makes an analogy between this war and the Vietnam war,” but if I stop there, I’ve only identified the logical appeal. I’d need to go on: “…in order to suggest that this war will be just as unwinnable as that one and that we, therefore, ought not wage it.”