 101ψ = 1000ψ

With base e the natural logarithm behaves like the common logarithm as ln(1e) = 0, ln(10e) = 1, ln(100e) = 2 and ln(1000e) = 3.The base "e" is the most economical choice of radix β > 1 , where the radix economy is measured as the product of the radix and the length of the string of symbols needed to express a given range of values.Base π can be used to more easily show the relationship between the diameter of a circle to its circumference, which corresponds to its perimeter; since circumference = diameter × π, a circle with a diameter 1π will have a circumference of 10π, a circle with a diameter 10π will have a circumference of 100π, etc.