Logarithm of a number will have an “integral” part and a “decimal” part. The integral part of the logarithm of a number is called the “CHARACTERISTIC” and the decimal part of the logarithm is called the “MANTISS”.
Logarithms are defined only for positive numbers. There are no logarithms defined for zero or negative numbers.
Logarithms can be expressed to any base. Logarithms from one base can be converted to logarithms to any other base. (One of the formulae given below will help in this conversion). However, there are two types of logarithms that are commonly used.
Natural Logarithms or Napierian Logarithms:
These are logarithms expressed to the base of a number called “e”.
Common Logarithms:
These are logarithms expressed to the base 10. For most of the problems under LOGARITHMS, it is common logarithms that we deal with. In examination also, if logarithms are given without mentioning any base, it can normally be taken to be logarithms to the base 10.
Thus, if a power x=N, then x=loga N (read as log N to the base a). This is the basic definition of a logarithm.
The basic definition of a logarithm is very useful in solving a number of problems on logarithms.
Example: 216=6 cube can be expressed as log6 216=3.
Logarithm problems are very useful for all competitive exams.
