A Logarithm in mathematics is a number that shows how many times a base number is multiplied by itself to produce a third number. 

The idea of logarithms is to reverse the operation of exponentiation, that is, raising a number to a power. For example, the third power (or cube) of 2 is 8, because 8 is the product of three factors of 2.

The logarithm to base 10 (that is b = 10) is called the common logarithm and has many applications in science and engineering. The natural logarithm has the number e (≈ 2.718) as its base and it's popularly used in mathematics and physics, because of its simpler derivative. The binary logarithm uses base 2 (that is b = 2) and is commonly used in computer science.

vCalc logarithm library contains equation of logarithmic identities and logarithmic properties