with base 10, what i’m asking is there a property or something that explains this?
5 Answers

500 = 1000 / 2

log(500)
=log(1000/2) replace 500 with 1000/2
=log1000log2 use the log property to change the fraction to a difference
=3log2 replace log1000 with 3

The answer is already been posted.
It is because log(1000/2) is the same as log(1000)log(2) [if you remember your properties)
Then log(1000) is 3
so it ends up
3 – log (2)

3 log2 = 3*log10 – log2
= log10^3log2
= log1000log2
=log1000/2
=log500
because logm logn= logm/n dats a basic rule

There’s no property to explain this. Probably just a coincedence.