A short note here for those who may not have used logarithms before, or are just a bit rusty.

If a number, a, is expressed as a power of another number, b ( if a = bn ), then 'n' is said to be the logarithm of a to base b, written logba. 'Common' logarithms are to base 10.

In mathematics and the sciences, 'natural' or 'Napierian' logarithms are often used as they can simplify calculations. These are logarithms to a base 'e', a number derived from the sum of the infinite series:

e = 1 + 1/1 + 1/1x2 + 1/1x2x3 + 1/1x2x3x4 + etc and e = 2.71828

Such a number may not appear at first sight to simplify anything! However, as this is not a book on maths, please just accept our word for it that it does.

Many hand-held calculators have buttons for both 'common' and 'natural' logarithms, marked LOG (base 10) and LN (base e) respectively. The relationship between the two types of logarithm is LOG(X) = 0.4343 x LN(X)

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