cogent
Clear, logical, and very convincing, especially as an argument.
Cogent means clear, logical, and convincing. When you make a cogent argument, you present your ideas in a way that makes sense and persuades people to see things your way. The evidence fits together, the reasoning flows smoothly, and the conclusion feels solid.
Imagine you want to convince your parents to let you get a dog. A cogent case would include specific points: you'll walk it every day after school, you've researched which breeds work well in apartments, you've saved money for supplies, and you'll handle the feeding schedule. Each reason supports the next, and together they make a strong case. A weak argument might just be “I really want one!” repeated over and over.
Scientists make cogent explanations of their discoveries. Lawyers present cogent cases in court. When your teacher asks you to explain your answer on a math problem, they want a cogent explanation that shows your logical steps clearly.