The logarithm of a number is the power to which a given number has to be raised to give a wanted result.
Example:
Given the number b = 5 and the wanted result 125. To which power has 5 to be raised to give the result 125? The answer is 3, since 53 = 125. The number b is called the base of the logarithm. The notation is log5125 = 3, or in words: The logarithm of 125 to the base 5 is 3.
The early Indian mathematicians had developed the series of numbers for logarithms to the base 2 as a sequence of square roots:
If 2x = 4, then x equals 2, which is the square root of 4.
If 2x = 16, then x equals 4, which is the square root of 16.
If 2x = 256, then x equals 16, which is the square root of 256.
The theory of logarithms can be extended to results that are fractions or irrational numbers. Indian texts showed methods to find logarithms such as log28 (which is 2 times the square root of 2).