logical
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logical
In accordance with the rules of logic; consistent, reasonable, and coherent.
Deine Argumentation ist nicht logisch, da die Schlussfolgerung nicht aus den Prämissen folgt.
Your argument is not logical, because the conclusion does not follow from the premises.
The adjective 'logisch' (logical) derives directly from the noun 'die Logik' (logic). If you know the noun, you can easily infer the meaning of the adjective.
Sein Plan war von Anfang bis Ende logisch aufgebaut.
His plan was logically structured from beginning to end.
As a standalone answer, 'Logisch!' (Of course!) is a colloquial expression of agreement and means 'Na klar!' (Sure!) or 'Selbstverständlich!' (Of course!). In this use, it is very informal.
Kommst du heute Abend zur Party? – Logisch, das lasse ich mir nicht entgehen!
Are you coming to the party tonight? – Of course, I wouldn't miss it!
In its main meaning, 'logisch' (logical) is often used to describe thought processes and their results. Typical combinations are 'eine logische Schlussfolgerung' (a logical conclusion), 'ein logischer Schritt' (a logical step), or 'logisch denken' (to think logically).
Nach der Analyse der Daten war die Kündigung des Projekts die einzig logische Konsequenz.
After analyzing the data, terminating the project was the only logical consequence.
natural / of course
'natürlich' and 'logisch' can both express agreement and mean roughly 'sure' or 'of course'. 'natürlich' is very general and fits when you definitely allow, confirm, or expect something. 'logisch' often sounds more colloquial and emphasizes more strongly that something is reasonable or follows from a reason. Learners may confuse the words because both can be used as a short answer to a question. If you are agreeing in a friendly way, 'natürlich' is often more neutral. If you want to say that something clearly follows from the situation, 'logisch' works well.
Wenn der Zug ausfällt, ist es logisch, dass viele Leute zu spät kommen.
If the train is canceled, it is logical that many people will arrive late.
Natürlich helfe ich dir nach dem Unterricht mit den Aufgaben.
Of course I'll help you with the assignments after class.