A common misconception regarding mileage logs is that you need to have a beginning and ending odometer reading for each mileage log you record. That would require you to write down your beginning and ending mileage each time you get in and out of your car. An odometer reading is only necessary at the end of each year (which becomes the beginning odometer reading for the next calendar year). Any “updated” odometer readings during the year, especially from third party service records, become corroborating evidence to support your vehicle use claims.
What should you do if you don’t have a complete mileage log for the entire year? Partial records can be useful to a tax preparer as the IRS allows sampling for some deductions. Sampling can be helpful if you can demonstrate by other evidence that the periods for which an adequate record is kept are representative of the use throughout the tax year.*
Re-creating mileage logs for gaps in your record or for periods of time where logs were not kept are done most effectively using a calendar to confirm where you traveled for business. The best source for a starting odometer is to estimate it from an oil change receipt or other service receipt which usually contains an odometer reading for that point in time.
You should consult with your tax professional to see how this applies to your specific tax circumstances.
Source: IRS Publication 463 Travel, Entertainment, Gift, and Car Expenses; Chapter 5 Recordkeeping; * “What if I Have Incomplete Records?” Sampling (including example).