Logarithms and Progressions in CAT: Complete Quantitative Aptitude Guide

Logarithms and Progressions in CAT can be directly solved using formulas provided on this page. With 3-4 days of focused practice, you can become well-versed in concepts like simplification, equations, and inequalities and maximize your scores in the QA section.

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Logarithms and Progressions in CAT Important Formulas
Preparation Tips for Logarithms and Progressions in CAT

Logarithms and Progressions in CAT can be considered vital concepts for solving a significant number of questions from Algebra. Important concepts under Logarithms include definition and properties of logarithms, Logarithmic functions and their graphs, change of base formula, applications of logarithms in exponential equations. Under Progressions, definitions and properties of Arithmetic Progression, Geometric Progression, Harmonic Progression, Nth term and sum of AP and GP, Arithmetic Geometric Progression, Sum of standard series, Arithmetic Mean, Geometric Mean and Harmonic Mean and their properties will be covered. 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

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

If x>0 and b is a constant (b≠1), then y=log _b x if and only if x=by.

In the equation y=log _b x, y is referred to as the logarithm , b is considered the base , and x is the argument.

log⁡ _a b implies the power to which ‘a’ must be raised to get ‘b’.

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 .

Arithmetic Progression (AP): Each term differs by a constant (common difference).

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, the next 3–4 days to get well-versed with Progressions. This way, you will not get fatigued from practising the same topics daily and your interest will remain sustained in the CAT preparation.
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, advanced Logarithm CAT questions PDF, mixed AP problems, mixed GP problems, Series & Progressions together. Solve timed 30-questions 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, application) on whichever topics or tricky formulas you frequently make errors in.

To further strengthen your preparation, assign 2–3 sessions per week for each topic- logarithms and progressions. In each session you must revise the concepts, memorize the important formulas, and practice questions with a higher difficulty level. Note down all the formulas in a single page to ensure quicker revision.

Related Links: 

How Many Questions to Attempt in CAT for 99 Percentile?	CAT Previous Year Question Papers PDF
Most Repeated Questions in CAT Exam

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