How do you estimate what consecutive integers log16 is between

Question

I need to show I estimate what consecutive integers log16 is between

Answer 1

If you're working with logs to base 10, you simply count how many digits there are in the integer part of the number. 16 has two digits. Now we subtract 1 from 2 to get 1. 1 is log₁₀10, and 16 is bigger than 10. log₁₀100=2, and since 16 lies between 10 and 100 its log lies between 1 and 2.