SAS Regression - Offset with log or natural log?

I am attempting to builds some count regression models to compare healthcare utilization between cases and controls with different follow-up times.

I was told by our lead statistician that I should offset with the log base 10 years to adjust for different follow up times. But in every example I've seen the offset option is equal to natural log of years.

Which is the correct method?

Please note: In SAS New_variable = log(old_variable) automatically uses natural log (for log base 10 the command is n = log10(x)).

Thanks in advance for the help.