If you operate more than 100 air miles from your base of operations, or you do not return daily to your home terminal then you will need to keep a log book.
If you stay within the 100 air mile limit and return to your home terminal then you may keep track of your hours worked on a time card, pay sheet, etc. You still can use a log book if you want, and it would be adviseable if from time to time you travel away from that 100 mile radius and/or do not return home for any given night.
Fmcsa regs 395