Learn the Class 9 Madhyamik Mathematics Logarithm Formulas with easy explanations, and solved examples. This page covers exponential and logarithmic forms, power rule, change of base formula, product rule, quotient rule, common logarithms, and important logarithmic properties for quick revision and exam preparation.
Chapter 21 – Logarithm | Class 9 Flash Formula
Different Forms in Logarithm
(i) ab = n is called the Exponential Form
(ii) logan = b is called the Logarithmic Form
Example
2³ = 8
Therefore, log₂8 = 3
Power Rule
loga(nx) = x logan
Example :
log₂(8²) = 2 log₂8
= 2 × 3
= 6
Change of Base Formula
logab = \text{log b}\over \text{log a}
Example :
log₂8 = \text{log 8}\over \text{log 2}
= \text{log 2}^3\over \text{log 2}
= \text{3 log 2}\over \text{log 2} = 3
Product Rule
loga(m × n) = logam + logan
Example :
log₂(4 × 8) = log₂4 + log₂8
= 2 + 3
= 5
Quotient Rule
loga(m ÷ n) = logam − logan
Example :
log₂(16 ÷ 4)
= log₂16 − log₂4
= 4 − 2
= 2
Logarithm of the Base
logaa = 1
Example :
log55 = 1
Remember
(i) Logarithms to the base 10 are called Common Logarithms.
(ii) If no base is given, the base is assumed to be 10.
(iii) log₁₀1 = 0 and log₁₀10 = 1
(iv) If logₐx = logₐy, then x = y
You have reached the end.