How to Crack Logarithms and Progressions Questions in CAT Quantitative Aptitude

Logarithms and Progressions in CAT are important topics from Algebra. You must strengthen your conceptual clarity of definition and properties of Logarithms along with functions and their graphs. Under Progressions, definitions and properties of Arithmetic Progression, Geometric Progression, Harmonic Progression, are some of the key topics that are targeted in CAT Exam . To prepare effectively for these topics, you must opt for in-depth practice by referring to PDFs of formulas, CAT-specific tricks, previous year questions, solved examples, and chapter-wise online practice tests. Create a personalised CAT formula sheet and regularly solve mock tests and PYQs in a timed manner to simulate the exam environment.

Also Read: Important Formulas for CAT

Logarithms and Progressions in CAT Important Formulas

Logarithms are the inverse of exponentiation. 1-2 questions can be expected from Logarithms in the CAT exam each year.

Logarithmic Identities

• Log b(xy) = log bx + log by
• Log b(x/y) = log bx – log by
• Log b(x^p) = p log bx
• Log b1 = 0
• Log bb = 1
• Log b(x) = 1 / log x(b)
• Change of base formula: log b(x) = log a(x) / log a(b)
• Common logarithm: log10(x) = log(x)
• Natural logarithm: log e(x) = ln(x)
• log _a xy = log _a x + log _a y
• log _a (x/y) = log _a x – log _a y
• log _a x ^m = mlog _a x
• log _{a ⁿ} x ^m = m/nlog _a x
• log _a x = 1/log _x a
• log _a a = 1
• log _a 1 = 0
• a ^{log _a m} = m

Logarithm Inequality

• If a > 1, p > 1 ⇒ log _a p > 0
• If 0 < a <1, p > 1 ⇒ log _a p < 0
• If a > 1, 0 < p < 1 ⇒ log _a p < 0
• If p > a > 1 ⇒ log _a p > 1
• If a > p >1 ⇒ 0 <log _a p <1
• If 0 < a < p < 1 ⇒ log _a p < 1
• If 0 < p < a < 1 ⇒ log _a p > 1
• If log _m a > b ⇒ {a > m ^b , if m > 1 a < m ^b , if 0 < m < 1
• log _m a < b ⇒ {a < m ^b , if m > 1a > m ^b , if 0 < m < 1
• log _p a > log _p b ⇒ a ≥ b if base p is positive and >1 or a ≤ b if base p is positive and < 1 e., 0<p<1

Progressions

A sequence of numbers that follows a particular rule or pattern is referred to as Progressions. 2-3 questions can be expected from this topic in the CAT 2025 exam .

• Formula for n -th term: a _n = a ₁ +(n−1)d

• Sum of first n terms: S _n = n/2[2a ₁ +(n−1)d]

• Geometric Progression (GP): Multiplication of each term by a constant (common ratio).

  • Formula for n -th term: a _n = a ₁ r ⁿ⁻¹

  • Sum, when r≠1: Sn = a ₁ − 1−r ⁿ / 1 - r

Harmonic Progression (HP): Reciprocal of an arithmetic progression which is less common in CAT but important for completeness
Special Series

Preparation Tips for Logarithms and Progressions in CAT

To be able to solve maximum questions from Logarithms and Progressions in CAT, you must draft a preparation plan strategically involving concept-building, revision, and mock tests.

• The first 2-3 months of CAT preparation must be allocated for covering all the foundational topics of Quant including both logarithms and progressions, to understand the concepts thoroughly and become competent enough to solve advanced problems.
• After this, you can opt for more focused preparation by dedicating 3–4 days to the intense practice of Logarithms, and the next 3–4 days to get well-versed with Progressions. This way, you will not become fatigued from practicing the same topics daily, and your interest in CAT preparation will remain sustained.
• The first week must be dedicated to strengthening the basics from NCERTS by focusing on topics like Exponents & Log Foundations, Laws of Logarithms, Change of Base & Properties, Logarithmic Equations, AP, GP, and HP. Ensure that you do not ignore Progressions since they can be regarded as scoring topics.
• The second week must be allocated for mastering CAT-level problems and formulas. The focus areas for this week should be mixed Log problems, the advanced Logarithm CAT questions PDF, mixed AP problems, mixed GP problems, Series & Progressions together. Solve timed 30-question sets over a duration of 60 minutes and practise CAT previous year questions involving series simplification, mixed AP+GP problems, application of GP in finance/interest, log-based inequalities, equations, etc.
• Solve mixed-topic CAT mocks and previous year question papers weekly to identify your strengths and weaknesses, reinforce learning, and determine your readiness to tackle integrated CAT problems. In the last 2-3 months, target specific topics for rapid revision based on mock test analysis, and allocate extra short sessions (involving MCQs, conceptual, and application) on whichever topics or tricky formulas you frequently make errors in.