Logarithms - Aptitude Concepts (Important Facts And Formulae)

IMPORTANT FACTS AND FORMULAE

I. Logarithm: If a is a positive real number, other than 1 and am = X,
   then we write: m = loga x and we say that the value of log x to the base a is m.

Example:
(i) 103 = 1000 => log10 1000 = 3
(ii) 2-3 = 1/8 => log2 1/8 = - 3
(iii) 34 = 81 => log3 81=4
(iiii) (.1)2 = .01 => log(.l) .01 = 2.


II. Properties of Logarithms:

1. loga(xy) = loga x + loga y

2. loga (x/y) = loga x - loga y

3.logx x=1

4. loga 1 = 0

5.loga(xp)=p(logax) 1

6. logax =1/logx a

7. logax = logb x/logb a=log x/log a.

Remember: When base is not mentioned, it is taken as 10.


III. Common Logarithms:

Logarithms to the base 10 are known as common logarithms.


IV. The logarithm of a number contains two parts, namely characteristic and mantissa.

Characteristic: The integral part of the logarithm of a number is called its characteristic.

Case I: When the number is greater than 1.
             The characteristic is one less than the number of digits in the left of the decimal point in the given number.

Case II: When the number is less than 1.
               The characteristic is one more than the number of zeros between the decimal point and the first significant digit of the number and it is negative.

Instead of - 1, - 2, etc. we write, 1 (one bar), 2 (two bar), etc.

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