Hello, my name is Ben and it is my pleasure to assist you with your question today.
The log book will be the property of whoever purchased it, unless they had subsequently gifted it to someone else, in which case the recipient would have become the legal owner. It would not automatically belong to the boat's owner, even if the contents within it were aimed at the boat or the journeys it made. In addition, the person who made the actual entries could argue that they have some copyright over it if they can show that what they wrote was an original literary work, of which they were the creator. However, that would not change the legal owner of the actual log book itself and they can only argue over the contents of the book.
Has this answered your query?