Arrest follows firewood in a diary (3-4)

'a diary' is the definition.
I know nothing about this answer so I can't tell whether this works.

'arrest follows firewood' is the wordplay.
'arrest' becomes 'book' (book can informally mean to arrest).
'follows' is a charade indicator (letters next to each other).
'firewood' becomes 'log' (log is a kind of firewood).
'book' put after 'log' is 'LOG-BOOK'.

'in' acts as a link.

Can you help me to learn more?