September 5th, 2016

In Technology

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# 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: lawrence@krubner.com, or follow me on Twitter.

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

### Post external references

- 1

https://en.wikipedia.org/wiki/Logarithmic_growth

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