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Logarithms — Revision Notes

CMAT · Quantitative Techniques & Data Interpretation

Free Logarithms revision notes for CMAT Quantitative Techniques & Data Interpretation 2026 — key concepts, formulas, and definitions for quick revision.

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An illustration showing the relationship between logarithmic form (log_a m = x) and exponential form (a^x = m), highlighting the constraints on 'a' and 'm'.
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Revision Notes — Logarithms

Key concepts, formulas, and definitions from Logarithms for CMAT Quantitative Techniques & Data Interpretation preparation.

Key Topics to Revise

1

Definition and Basic Concepts

  • If a^x = m, then x = log_a(m), where 'a' is the base, 'm' is the argument, and 'x' is the logarithm
  • Logarithm is only defined for positive real numbers as arguments
  • Base 'a' must be positive and not equal to 1
2

Laws of Logarithms

  • Product Law: log_a(mn) = log_a(m) + log_a(n)
  • Quotient Law: log_a(m/n) = log_a(m) - log_a(n)
  • Power Law: log_a(m^n) = n·log_a(m)
3

Base Change Rule

  • Allows conversion between different logarithmic bases
  • Essential for solving problems with mixed bases
  • Formula: log_a(b) = log_c(b)/log_c(a)
4

Characteristic and Mantissa

  • Any logarithm consists of integer part (characteristic) and decimal part (mantissa)
  • Characteristic can be positive, negative, or zero
  • Mantissa is always written as positive

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Key Concepts

If a^x = mTwo essential propertiesThree fundamental lawsLogarithms with base 10 are calledEvery logarithm consists of two parts

Frequently Asked Questions

What topics are covered in Logarithms for CMAT?
Logarithms is an important chapter in CMAT Quantitative Techniques & Data Interpretation. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Definition and Basic Concepts, Laws of Logarithms, Base Change Rule, Characteristic and Mantissa.
How important is Logarithms for CMAT?
Logarithms is a frequently tested chapter in CMAT Quantitative Techniques & Data Interpretation. Questions from this chapter appear regularly in previous year papers. There are 58 practice questions available for this chapter.
How to prepare Logarithms for CMAT?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.

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