In any event, regardless of which method in respect to the feeding of prisoners is selected by the board of supervisors, the sheriff shall maintain a log, showing the name of each prisoner, the date and time of incarceration and release, to be posted daily, which shall record the number of meals served to prisoners at each mealtime, and the hours of the day served, and shall make affidavit as to the correctness thereof and file the same monthly with the board of supervisors. Such log shall remain on file with the board of supervisors as other records of said board and shall be made available to the state department of audit upon request. No claims for the cost or expenses of feeding prisoners shall be approved by the board of supervisors for any month unless and until such log for that month is filed.