The base b logarithm of x is a value y such that by = x
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Common
Logarithms can be taken to any base. Common logarithms are logarithms taken to base 10; it is sometimes abbreviated to lg. Natural logarithms are logarithms taken to base e (= 2.71828....); it is usually abbreviated to ln.
A logarithm can not be converted in to an exponential, as an exponential is defined for all real numbers, while a logarithm is only defined for numbers greater than zero. However, a logarithm can be related to an exponential by the fact that they are inverses of each other. e.g. if y = 2^x the x = log2y
The logarithm of [ 1 x 109 ] is 9.00000
If a^x = n, where a is a positive real number other than 1 and x is a rational number then logarithm is defined as, logarithm of n to the base a is x. Then is written as log n base a = x.