Base 10 numbers need log(10) digits to be described

(written by lawrence krubner, however indented passages are often quotes). You can contact lawrence at:

I’m sure I knew this example once, but I’d completely forgotten it, and it is so perfectly obvious when we talk to non-technical people and they ask for an example of what logarithmic growth looks like:

In mathematics, logarithmic growth describes a phenomenon whose size or cost can be described as a logarithm function of some input. e.g. y = C log (x). Note that any logarithm base can be used, since one can be converted to another by multiplying by a fixed constant.[1] Logarithmic growth is the inverse of exponential growth and is very slow.[2]
A familiar example of logarithmic growth is the number of digits needed to represent a number, N, in positional notation, which grows as logb (N), where b is the base of the number system used, e.g. 10 for decimal arithmetic