Math Logarithm Properties

Math Logarithm Properties

If a is positive real number, other than 1 and cn = m, then we say: n = logcm and we say that the value of logm to the base c is n.

 

  • 103 1000 = log10 1000 = 3.
  • 34 = 81 = log 3 81 = 4
  • (.1)2 = .01 = log(.1) .01 = 2

 

Logarithm Properties :

 

  • Product Rule : loga (xy) = loga x + loga y
  • Quotient Rule :  loga (x/y) = loga x – loga y
  • Logarithm of any quantity same base is unity i.e, log x X = 1
  • Logarithm of 1 to any base Zero i.e, loga 1 = 0
  • loga (xn) = n(loga x)
  • loga x = 1 / logx a
  • Change of Base Rule : loga x = logb x / logb a = log x / log a

 

 

  • logb N = logb a . loga N,                       ( a > 0, a ≠ 1, N>0 )

 

  • logb a = 1 / loga b ,                                    (a > 0, a ≠ 1)

 

 

  1. logb 1 = 0
  2. loga a = 1
  3. logb 0 = { – ∞, b > 1, + ∞, b < 1 }

 

 

Decimal Logarithm

 

  • log10 N = lgN     ( b = 10)

 

  • lgN = x ⇔ 10x = N

 

Natural Logarithm

 

loge N = InN

InN = x ⇔ ex = N

 

 

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