30+ CAT Logarithm Questions (with Answers & Downloadable PDF)

CAT Logarithm questions are a regular part of the QA section and can be quite easy to score if your basics are clear. In this section, you’ll find 30+ practice questions, starting from easy ones and moving up to CAT-level questions. You’ll also get the answers, a quick formula sheet, and a free PDF to help you practise.

• Cracking CAT Exam requires a strong grasp of quantitative aptitude, and logarithm questions often feature prominently.
• Practising previous-year CAT log questions gives you an idea of the section's difficulty level. We provide detailed explanations and strategies to tackle various logarithm questions for CAT.

If you’re preparing for CAT and looking for Logarithm questions, this set can help you practise the most common question types. It covers topics such as nested logarithms, change of base, and logarithmic equations, along with step-by-step solutions to help you understand how to solve them.

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In this blog, we will demystify logarithms as covered in the CAT Syllabus, provide a deep dive into logarithm-related CAT questions, and offer proven strategies to master the topic. By the end of this post, you will be better equipped to approach logarithm questions in the CAT exam with confidence, having a clear understanding of the concepts and strategies that frequently appear in the CAT syllabus.

CAT Exam 2026 is expected to be conducted on 29 November 2026 (Sunday). Read on to get the most important CAT logarithm questions asked in CAT previous year papers.  

What are CAT Logarithm Questions?

CAT Logarithm Questions refer to problems based on logarithmic concepts that are asked in the Quantitative Aptitude (QA) section of the Common Admission Test (CAT) — a national-level MBA entrance exam conducted by the IIMs.

Download Logarithm Questions and Answers PDF

Key Features of CAT Logarithm Questions 2026:

• These logarithm CAT questions test your understanding of logarithmic rules, properties, and simplifications.
• They often appear in the form of equations, expressions, or word problems that require logical and algebraic manipulation.
• Generally, you can expect 1–3 questions on logarithms in the CAT exam each year.

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Important Links

CAT Exam Analysis	CAT PYQs	CAT 2020 Question Paper
CAT Number System Question	CAT 2021 Question Paper	CAT 2022 Question Paper
CAT 2025 Question Paper	CAT 2024 Question Paper	CAT 2023 Question Paper

15+ Important CAT Logarithm Questions to Practice Now

Here are some of the most important CAT previous year logarithm questions that can help you get an idea about the difficulty level. Let's solve them:

1. For a real number a, if (log₁₅a)(log₃₂a)=4, then a must lie in the range:

A) 2 < a <3

B) 3 < a <4

C) 4 < a < 5

D) a > 5

Answer: D

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6. If log₂(5+log₃a)=3 and log₅(4a+12+log₂b)=3, then a+b = :

A) 59

B) 40

C) 32

D) 67

Answer: A

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7. If log₁₂81 = p then 3^((4−p)/(4+p)) = :

A) log₄16

B) log₆16

C) log₂8

D) log₆8

Answer: B

8. If log₂log₇(x²−x+37)=1, a possible x is:

A) 3

B) 5

C) 4

D) None

Answer: C

Check Important Subject Level Question Paper Links

Arithmetic Questions	Arithmetic Syllabus	Profit & Loss Questions
Averages Questions	Time & Work Questions	Time-Speed-Distance
Mixture & Alligation	Games & Tournaments	Calculate Percentage

9. If (log₂x)²−6log₂x+12 = u and xᵘ = 256, how many solutions?

A) none

B) one

C) two

D) three

Answer: B

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10. If logᵧx = (a·log_z y) = (b·logₓz) = ab, which (a,b) is NOT possible?

A) (−2, ½)

B) (1,1)

C) (0.4, 2.5)

D) (π, 1/π)

Answer: A

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11. If log₄a = 3, what is log₂a?

A) 3

B) 6

C) 12

D) 9

Answer: B

12. If log₃x + log₃(x−8) = 2, what is x?

A) 10

B) 8

C) 9

D) 11

Answer: C

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13. If log₅25 + log₅125 = x, then x =?

A) 5

B) 4

C) 3

D) 2

Answer: A

Read more: Practise Number System CAT Questions 

14. If logₓ64 = 3, then x is:

A) 3

B) 2

C) 4

D) 8

Answer: C

15. If log₂x = 5, then x =?

A) 32

B) 2⁵

C) 25

D) 20

Answer: A

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16. What is log₈16 + log₄8?

A) 3

B) 2

C) 2.5

D) 4

Answer: A

17. If logₓ16 = 4, then x =?

A) 2

B) 4

C) 8

D) 16

Answer: A

18. What is log₉81?

A) 2

B) 3

C) 1.5

D) 4

Answer: A

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19. If log₄x = 3, then x =?

A) 16

B) 64

C) 64

D) 128

Answer: B

20. If x and y positive and log₅(x+y)+log₅(x−y)=3, and log₂y − log₂x = 1−log₂3, find xy.

A) 150

B) 25

C) 100

D) 250

Answer: A

21. Which of the following is the correct value of log⁡2(32)\log_2(32)log2​(32)?

A) 4
B) 5
C) 6
D) 3

Answer: B

22. What is the value of log⁡10(100)\log_10(100)log1​0(100)?

A) 2
B) 3
C) 1
D) 4

Answer: A

23. If log⁡2(x)=5\log_2(x) = 5log2​(x)=5, what is the value of xxx?

A) 10
B) 16
C) 32
D) 64

Answer: C

CAT Logarithm Questions Weightage Over the Past 3 Years

Year	Slot 1	Slot 2	Slot 3	Total Approx
CAT 2024	2	3	2	6–7
CAT 2023	2	2	3	6–7
CAT 2022	3	2	2	6–7

Important Formulas for CAT Logarithm Questions 2026

🔹 Logarithmic Formulas

• log_a(x * y) = log_a(x) + log_a(y)
• log_a(x / y) = log_a(x) - log_a(y)
• log_a(x^p) = p * log_a(x)
• log_a(x^(1/p)) = (1/p) * log_a(x)
• log_b(x) = log_k(x) / log_k(b)
• log_a(1) = 0, log_a(a) = 1, log_x(a) = 1 / log_a(x)

🔹 Indices Laws

• x^m * x^n = x^(m+n)
• x^m / x^n = x^(m−n)
• (x^m)^n = x^(m·n)
• 1 / x^m = x^(−m)
• (x*y)^m = x^m * y^m
• (x/y)^m = x^m / y^m

🔹 Surds Essentials

• √a * √b = √(ab)
• Like radicals can be added or subtracted directly.

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Why Logarithms Are Important for CAT 2026

Logarithms are included in the Quantitative Ability section of CAT 2026, and they frequently appear in the form of word problems or algebraic expressions. Logarithm CAT questions often test your ability to manipulate logarithmic expressions and understand the properties of logarithms quickly. Having a clear grasp of the following concepts will give you an edge:

• Properties of logarithms
• Conversion between different logarithmic bases
• Solving logarithmic equations
• Simplifying expressions involving logarithms

Tips to Ace CAT Logarithms Questions Section 2026

• Remember the important formulas – Knowing the formulas well will save you a lot of time during the exam.
• Practise basic simplification – Get comfortable with powers, roots, and changing the base of logarithms.
• Make good use of the options – Since CAT has MCQs, try using options or back-solving when it makes the question easier.
• Revise regularly – Solve a few logarithm questions every week so you don’t forget the concepts.
• Practise with Surds and Indices – Logarithm questions can sometimes be mixed with these topics, so practise them together.

Conclusion

CAT Logarithm Questions 2026 are easy to conquer — provided you approach them with a conceptual and practical mindset. With just a couple of well-placed CAT log questions in the exam, this topic is low effort and high return. Bookmark this guide and keep the formula PDF handy for revisions.