Logarithms were invented as an aid to multiplication and division at a time when calculators and computers were not even in the realm of science fiction! Despite their long history the logarithm still has many uses not only in mathematics but in the fields of science and engineering.

Consider the equation:

a = bn

n is defined to be the logarithm of a to the base b, or:

n = logb a

The base b can be any number but in most cases is either 10 for what are known as 'Common Logarithms' or e (2.7182818...) for 'Napierian' or 'Natural Logarithms'. The base subscript is often omitted for base 10 logarithms and simple written as log (or just lg). As natural logarithms are a special case they are usually written as ln.

The following formulae may be useful when dealing with logarithms:

logb (x y) = logb x + logb y

logb (x/y) = logb x - logb y

logb (1/x) = - logb x

logb xy = y logb x

logb yÖ x = 1/y logb x

The inverse function or anti-log is simply a matter of raising the base to the power of the logarithm. Thus:

antilogb x = alogb x = bx

antilog10 x = alog10 x = 10x

antiloge x = aloge x = ex

The logarithm of any value in any base may be determined by using the following formula:

logb x = loga x / loga b


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