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. This ths the Math Logarithm Properties.
- 103 1000 = log10 1000 = 3.
- 34 = 81 = log 3 81 = 4
- (.1)2 = .01 = log(.1) .01 = 2
Logarithm Properties :
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- 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)
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- 1. logb 1 = 0
- 2. loga a = 1
- 3. logb 0 = { – ∞, b > 1, + ∞, b < 1 }
Decimal Logarithm
- log10 N = lgN ( b = 10)
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- lgN = x ⇔ 10x = N
Natural Logarithm
loge N = InN
InN = x ⇔ ex = N
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