23 CHAP - 23 LOGARITHMS IMPORTANT FACTS AND FORMULAE I...

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23. LOGARITHMS IMPORTANT FACTS AND FORMULAE I. Logarithm : If a is a positive real number, other than 1 and a m = X, then we write: m = log a x and we say that the value of log x to the base a is m. Example: (i) 10 3 = 1000 => log 10 1000 = 3 (ii) 2 -3 = 1/8 => log 2 1/8 = - 3 (iii) 3 4 = 81 => log 3 81=4 (iiii) (.1) 2 = .01 => log (.l) .01 = 2. II. Properties of Logarithms: 1. log a (xy) = log a x + log a y 2. log a (x/y) = log a x - log a y 3.log x x=1 4. log a 1 = 0 5.log a (x p )=p(log a x) 1 6. log a x =1/log x a 7. log a x = log b x/log b a=log x/log a. Remember: When base is not mentioned, it is taken as 10. II. Common Logarithms: Logarithms to the base 10 are known as common logarithms. III. 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. In this case, the characteristic is one less than the number of digits in the left of the
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This note was uploaded on 08/13/2011 for the course FSD 011 taught by Professor Vinh during the Spring '11 term at Beacon FL.

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23 CHAP - 23 LOGARITHMS IMPORTANT FACTS AND FORMULAE I...

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