적다 is jotting something down rather than composing it: 메모장을 이렇게 해서 적어놨어요, 그냥 3이 좋아서 적어놨어요. The -아서/어서 gives the step or the reason before writing — 하루 동안 감사했던 거를 찾아서 적으면, 왜 거기다가 콕 집어서 적어주신 걸 보면. Note the phrase 알아서 적어주세요, "just put down whatever you like," where 알아서 leaves it to the other person's judgment. Be careful: 적다 is also the adjective "be few, be little," spelled exactly the same.