30+ Important CAT Logarithm Questions with Answers [PDF Download]

Overview: CAT Logarithm questions might look tricky, but they’re one of the most scoring areas in the CAT Quant section. With just 2–4 questions appearing every year, mastering logarithmic concepts can give you a significant edge in your percentile.

• Cracking the CAT exam requires a strong grasp of quantitative aptitude, and logarithm questions often feature prominently.

Download FREE Study Material for CAT Exam 2026 by Supergrads

• Practicing  Previous year CAT log questions gives you an idea about the difficulty level of the section. We provide detailed explanations and strategies to tackle various logarithm questions for CAT.

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

Read on to get the most important CAT logarithm questions asked in the CAT previous year papers

Check: How to prepare for Quantitative Aptitude for CAT exam?

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.

Get Solved Ratio and Proportion Questions for CAT – Free PDF Download

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

Check: Venn Diagram Practice Questions for CAT 2026 

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

A) 59

B) 40

C) 32

D) 67

Download CAT 2026 Geomery Questions [PDF Download]

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

A) log₄16

B) log₆16

C) log₂8

D) log₆8

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

A) 3

B) 5

C) 4

D) None

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

A) none

B) one

C) two

D) three

Click Here: Download CAT Arithmetic questions PDF with Solutions 

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)

Download 40+ Number Theory Practice Questions – Free PDF

11. If log₄a = 3, what is log₂a?

A) 3

B) 6

C) 12

D) 9

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

A) 10

B) 8

C) 9

D) 11

Use SuperGrads Free Resources 2026 Strategically

CAT VARC Mock Test 2026	Attempt a Free Mock test
CAT DILR Mock test 2026	Attempt a Free Mock test
CAT QA Mock Test 2026	Attempt a Free Mock test
CAT VARC Prep Videos 2026	Watch Now

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

A) 5

B) 4

C) 3

D) 2

Read more: Practise Number System CAT Questions 

14. If logₓ64 = 3, then x is:

A) 3

B) 2

C) 4

D) 8

15. If log₂x = 5, then x =?

A) 32

B) 2⁵

C) 25

D) 20

Access 60+ CAT Time and Work Q&A – Download Free PDF

16. What is log₈16 + log₄8?

A) 3

B) 2

C) 2.5

D) 4

17. If logₓ16 = 4, then x =?

A) 2

B) 4

C) 8

D) 16

18. What is log₉81?

A) 2

B) 3

C) 1.5

D) 4

Download Geometry Part 1 – 40+ CAT Questions [Free PDF]

19. If log₄x = 3, then x =?

A) 16

B) 64

C) 64

D) 128

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

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

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

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

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

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.

Access Free 30+ CAT VARC Sample Questions and Answers – Download PDF

Why Logarithms Are Important for CAT 2026

Logarithms are included in the Quantitative Ability section of the CAT, 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

• Know all formulas by heart – You can’t afford to waste time deriving.
• Practice basic simplifications, especially powers, roots, and conversions of bases.
• Use options smartly – CAT is MCQ-based, so try back-solving wherever possible.
• Revise weekly – Logarithms need repetition to master.
• Mix with Surds & Indices – CAT often combines concepts. 

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.