1. Chapter Three Logarithm
Afjal Hossain
Assistant Professor
Department of Marketing, PSTU

2. Definition of Logarithm
The logarithm of a number to a given base is the index or the power to which the base must be raised to produce that number.
Ex: If ax = n, then
A logarithm has three important/ integral parts:
Number (n)
Base (a)
Power/ Index/ Value of Logarithm (x)

3. Exercise !

4. Types of Logarithm
Natural Logarithm
The logarithm of a number to the base “e” (e=2.718) is called natural or Napierian logarithm. It is introduced by John Napier ( ). In theoretical calculations, the base “e” is used whereas for numerical calculations.
Common Logarithm
The logarithm of a number to the base “10” is called common or Briggsian logarithm. It is introduced by Henry Briggs ( ). It is also used in numerical calculation and it is most convenient. The tables that are given at the end of the book are all calculated with “10” as base. When no base is mentioned, it is understand to be “10” by the word logarithm we generally mean common logarithm.

5. Keep in Mind-I (General)
Product Rule: log(MN) = logM + logN {not logM x logN or, log(M+N) = logM + logN}
Division Rule: log = logM – logN {not logM logN or, log(M – N) = logM – logN}
Power Rule: logMN = N log M
log 0/
log 1/
log 10 = 1; log 100 = 2 etc.
If the log has same base & number then the value is equal one. Ex: l
Base of a logarithm can never be 0 or 1 or negative.

6. Keep in Mind-II (Changing)
[read as log m to the base a] l

7. Keep in Mind-III (Index + Others)

8. Keep in Mind-III (Index + Others)

9. Keep in Mind-III (Index + Others)

10. Components of a Logarithm: 2 Parts
Characteristics
The whole part or the integral part of a number is called characteristics. The characteristic of the logarithm of any number is less than 1. Ex: log 10 = 1
Mantissa
The decimal part of a number is called mantissa. The mantissa is always positive.

11. Exercise
Find the characteristics and mantissa for the logarithm of a number is

12. Antilogarithm
If x is the logarithm of a given number n with a given base then n is called the antilogarithm (antilog) of x to that base.