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Arithmetic Aptitude :: Logarithm

Logarithm - Important Formulas

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Logarithm:

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

Examples:

(i). 103 1000      log10 1000 = 3.

(ii). 34 = 81      log3 81 =

(iii) 2-3 = \(\frac { 1 } { 8} \)    log\(\frac { 1 } { 8} \)= -3

(iv) (.1)2 = .01    log(.1) .01 = 2.

2.Properties of Logarithms:

  1. loga (xy) = loga x + loga y

  2.  logx x = 1 

  3 .loga 1 = 0

 4. loga (xn) = n(loga x)

 5. loga  \([ \frac { x } { y } ]\) = loga x - loga y

 6 . loga x = \( \frac { logb X } { logb a} \) = \( \frac { log X } { log a} \)