Final Cover - For Printing

Module 68 : Logarithm

LOGARITHM

Logarithm
The concept of logarithm was introduced by a Scottish mathematician John Napier (1550 -
1617). John Napier together with Henry Briggs (1561-1631) constructed the ready to use
logarithmic tables which are also known as ‘ common logarithms’. Note that the base of all
the common logarithms is 10. Logarithm is another form of expressing a number in
exponential form.

1. Logarithm
   The logarithm of a number to a given base is the power to which the base is to be
   raised to equal the given number.

Consider the expression in exponential form, a = xm. In logarithmic form the given

expression can be rewritten as, logx a = m.

Note : 1. The base must always be positive and should not be equal to 1.

2. Logarithms are defined only for positive real numbers and not defined
   for 0 and negative numbers.

Eg.: Find the value of log 5125

Let log 5 125 = x

Therefore in exponential form, 5x = 125

That is, 5x = 5^3