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Math Logarithm Properties

Last Modified on August 10, 2022 by Admin

Math Logarithm Properties

If a is positive real number, other than 1 and cⁿ = m, then we say: n = logc^m 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 : log_a (xy) = log_a x + log_a y
Quotient Rule : log_a (x/y) = log_a x – log_a y
Logarithm of any quantity same base is unity i.e, log x _X = 1
Logarithm of 1 to any base Zero i.e, log_a 1 = 0
log_a (xⁿ) = n(log_a ^x)
log_a ^x = 1 / log_x a
Change of Base Rule : log_a ^x = log_b ^x / log_b ^a = log x / log a

log_b N = log_b a . log_a N, ( a > 0, a ≠ 1, N>0 )

log_b a = 1 / log_a b , (a > 0, a ≠ 1)

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

Decimal Logarithm

log₁₀ N = lgN ( b = 10)

lgN = x ⇔ 10^x = N

Natural Logarithm

log_e N = InN

InN = x ⇔ e^x = N

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One comment

Armstrong Oheneba Einstein says: June 8, 2019 at 1:19 pm
Thanks very much for your help and innovative means to aid students in learning maths easily

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Math Logarithm Properties

Decimal Logarithm

Natural Logarithm

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