Home > Math Shortcuts > Math Logarithm Properties

# 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. 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 :

• 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

1. 