Given a positive real number y, there is one and only one real number x such that ax = y, we call this number x as logarithm of y to the base a.
Logarithm gives the power to which the base is to raised to get the number.
Logarithms can be defined for any base.Logarithms defined to the base 10 and to the base e are tabulated and used more widely. Logarithms to the base 10 are called common logarithms and logarithms to the base e are called natural logarithms.
Many books follow the convention of writing natural logarithms as ln y and common logarithms as log y.
In mathematics books as logarithms are given for various bases, the base may be specified.
Some properties
1. loga1 = 0, a>0, and a ≠0
2. logaa = 1, a>0, and a ≠0
Good online material
http://tutorial.math.lamar.edu/Classes/Alg/LogFunctions.aspx
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