Logarithm Questions for CAT: Definition, Types, Formulas and Download Sample CAT Log Questions PDF

By BYJU'S Exam Prep

Updated on: September 13th, 2023

CAT Log Questions are one of the topics of the quantitative aptitude section of the CAT. Logarithm Questions for CAT have been consistently asked for the past few years, and the aspirants can expect at least 1-2 questions on this topic. The difficulty level may vary from easy to difficult; however, the aspirants need to understand the basic concepts and rules to solve CAR Log Questions.

Everyone knows that Logarithms are the opposite function of exponents. The concept of Logarithm Questions for CAT is based on the logarithm of a number with a base that is equal to another number. For example, If 102 is 100, then its Log10 100 will be 2. So, the aspirants appearing for the upcoming CAT must be well-versed in CAT Log Questions types and their concepts. In this article, BYJU’S Exam Prep experts have detailed all the concepts of CAT Logarithm Questions with examples to assist the aspirants in their preparation.

What are CAT Log Questions?

The Logarithm concept is based on the power by which a number can be increased to get other values. CAT Logarithm Questions can be solved based on the following properties:

  • Power rule: Logb Mp = P Logb M
  • Product rule: Logb MN = Logb M + Logb N
  • Zero Exponent Rule: Loga 1 = 0
  • Quotient rule: Logb M/N = Logb M – Logb N
  • Change of Base Rule: Logb (x) = ln x / ln b or Logb (x) = Log10 x / Log10 b

Apart from this, the aspirants must keep in mind that the CAT Logarithm Questions functions are the inverse functions of exponentiation. Note the point that is given below for conceptual clarity on the function of Logarithm Questions for CAT.

☛ See Also: CAT Registration

For x, a > 0, and a≠1, we can write the following expression:

  • y= Loga x, if x = ay

Thereby, the Logarithmic function will be as follows:

  • f(x) = Loga x

Go through the table that is given below to get a clear idea between Logarithms and Exponents.



52 = 25

Log5 25 = 2

102 = 100

Log10 100 = 2

43 = 64

Log4 64 = 3

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CAT Logarithm Questions Types

In most cases, the aspirants have to solve two types of CAT Log Questions, such as

  • Natural Logarithm: This is the base “e” logarithm, in which “e” represents Euler’s constant which is approximately equal to 2.71828.
  • Common Logarithm: This is the base “10” logarithm, represented as Log10.

Logarithm Questions for CAT PDF

Click on the link below to download CAT Log Questions PDF for free. Our experts have curated the past year’s CAT Question Papers and made a list of important Log Questions for CAT.

Download CAT Log Questions with Solutions

CAT Log Questions Examples

By curating the trends of CAT Quant Questions, our expert team has listed some examples of CAT Logarithm Questions here for the aspirants to help them understand the types and difficulty levels for Logarithm Questions for CAT.

Question 1:Find the value of x, if Log(x-1)+Log(x+1)=Log21



∴ Log(x-1)+Log(x+1)=0

∴ Log[(x-1)(x+1)]=0

As we know: Log 1= 0; we can write the following:

∴ (x-1)(x+1) = 1

∴ x2-1=1

∴ x2=2

Answer: x= √2 (The Log of a Negative Number is Not Defined)

Question 2:If Log (2^a × 3^b × 5^c) is the arithmetic mean of Log (2^2 × 3^3 × 5), Log (2^6 × 3 × 5^7), and Log(2 × 3^2 × 5^4), then a equals to [CAT 2017]

Answer: a=3

Solution: Log (2^a. 3^b. 5^c) = [Log (2^2.3^3.5) + Log (2^6.3.5^7) + Log (2.3^2.5^4)]/3

3 * Log (2^a. 3^b. 5^c) = Log (2^9.3^6.5^12)

Log (2^a. 3^b. 5^c)^3 = Log (2^9.3^6.5^12)

Log (2^3a. 3^3b. 5^3c) = Log (2^9.3^6.5^12)

3a = 9


The aspirants have to practice a lot to grasp CAT Log Questions as these questions appear tricky if not prepared well. Attend BYJU’S Exam Prep CAT Online Coaching to learn the important formulas and shortcut tricks to solve CAT Logarithm Questions.

Formulas for Logarithm Questions for CAT

There are certain formulas based on which the logarithm questions are answered in CAT Exam. Here, BYJU’S Exam Prep experts have listed down some common formulas to assist you in solving the CAT Log Questions.

  • Logb (mn) = Logb (m) + Logb (n)
  • Logb m√n = Logb n/m
  • Logb (m+n) = Logb m + Logb (1+nm)
  • Logb (xy) = y Logb (x)
  • Logb (m/n) = Logb (m) – Logb (n)
  • Logb (m – n) = Logb m + Logb (1-n/m)
  • m Logb (x) + n Logb (y) = Logb (xmyn)

☛ See Also: CAT Answer Key

Best Books to Prepare Log Questions for CAT

While preparing for Logarithm Questions for CAT, the candidates must follow the best CAT Books to make a complete preparation. Below are some important books you may follow to prepare CAT Log Questions effectively.

Log Questions for CAT Books


NCERT Mathematics Books (Class 6 to 10)


Quantitative Aptitude for Competitive Examinations

Abhijit Guha

Quantitative Aptitude for CAT

Nishit Sinha

Quantitative Aptitude

R.S. Aggarwal

Tips to Solve CAT Log Questions?

To solve Logarithm Questions for CAT, the candidates must have good knowledge of its related formula and concept. Knowledge of basic logarithms will help the candidates to solve CAT Logarithm Questions accurately. Following are some of the tips to prepare for CAT Log Questions:

  • The candidates should regularly practice and analyse mocks and previous year’s question papers. This will help them to solve CAT Log Questions accurately.
  • Candidates should have good knowledge of graphs to solve the questions on functions and graphs under Logarithm Questions for CAT.
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