When writers use a logical appeal (logos, or “word” in Greek), they appeal to the reader’s mind or intellect. This appeal relies on evidence that is factual, objective, clear, and relevant. Critical readers expect to find logical evidence that supports major claims and statements.
Example: If a writer were arguing for term limits for legislators, she wouldn’t want to base her argument on the evidence that some long-term legislators were or weren’t reelected (irrelevant) or that the current system is unfair to young people who want to get into politics (illogical). Instead, she might argue that the absence of term limits encourages corruption, using evidence of legislators who repaid lobbyists for campaign contributions with key votes.