"Han skriver i en personlig bog."
Translation:He writes in a personal book.
bog is an 'en' word and is singular (plural would have an -e ending), so it wouldn't have the t at the end. . . The grammar is right, my problem is that no one in Denmark has ever uttered this sentence.
en personlig bog to personlige bøger
I do not know of a situation where there would be a T in regards to a book.