23 CHAP

# 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 decimal point in the given number.

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