FACTS AND FORMULAE FOR LOGARITHMS QUESTIONS
Here is called as exponential function and it is a finite number for every .
Let a,b be positive real numbers then can be written as
(i) Natural Logarithm :
is called Natural logarithm or Naperian Logarithm, denoted by ln N i.e, when the base is 'e' then it is called as Natural logarithm.
e.g , ... etc
(ii) Common Logarithm : is called common logarithm or Brigg's Logarithm i.e., when base of log is 10, then it is called as common logarithm.
PROPERTIES OF LOGARITHM
CHARACTERISTICS AND MANTISSA
Characteristic : The integral part of logarithm is known as characteristic.
Mantissa : The decimal part is known as mantissa and is always positive.
E.g, In , the integral part of x is called the characteristic and the decimal part of x is called the mantissa.
For example: In log 3274 = 3.5150, the integral part is 3 i.e., characteristic is 3 and the decimal part is .5150 i.e., mantissa is .5150
To find the characteristic of common logarithm :
(a) when the number is greater than 1 i.e., x > 1
In this case, the characteristic is one less than the number of digits in the left of the decimal point in the given number.
(b) when the number is less than 1 i.e., 0<x<1
In this case the characteristic is one more than the number of zeros between the decimal point and the first significant digit of the number and is negative.
Instead of -1, -2, etc. we write, etc.