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If the IRS looked into this on your tax return, they probably would take issue based on personal vs. business use. The IRS would argue that you had to pay for the mileage out of your own pocket regardless of whether it had the advertising posted on the car.
The following is an exert from the IRS website:
Advertising display on car. Putting display material that advertises your business on your car does not change the use of your car from personal use to business use. If you use this car for commuting or other personal uses, you still cannot deduct your expenses for those uses.
If you have any further questions, please do not hesitate to contact me.
If you are utilizing the car for business purposes, you may deduct mileage for those miles regardless of the advertising on the car. The only caution is that the IRS requires you to keep a log of these miles (i.e. date, location to location, number of miles....). The IRS would want to see this information if you were ever audited and this expense was subject to the inquiry.
and that log can just be in like in a reg note book corect
i am disatisfied with this answer and want a 100% refund
I am not sure why you are don't agree. Yes, it can be in a regular note book. However, if audited, presentation is everything.