Log CAT Questions: Definition, Types, Formulas and Examples

By Aditi Joshi|Updated : April 6th, 2022

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

Everyone knows that Logarithms are the opposite function of exponents. The concept of Log CAT questions 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 exam must be well-versed with Logarithms and its concepts. In this article, our experts have shared concepts of CAT Logarithm Questions with examples to assist the aspirants in their preparation.

Table of Content

What are Log CAT Questions?

The Logarithm concept is based on the power by which a number can be increased to get other values. Log CAT questions can be solved on the basis of 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 Logarithm's functions are the inverse functions of exponentiation in CAT. Note the point that is given below for conceptual clarity on the function of Log CAT Questions.

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

Types of Log CAT Questions

In most of the cases, the aspirants have to solve two types of CAT Logarithm 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.

Formulas for Log CAT Questions

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 Log CAT 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)

Download CAT Log Questions with Solutions

Log CAT Questions: Examples

By curating the trends of CAT QA 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 Log CAT Questions.

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 Log CAT questions as these questions appear tricky if not prepared well. Attend BYJU’S Exam Prep online classes to learn the important formulas and shortcut tricks to solve CAT Logarithm Questions.

Also Read:- How much time is required to prepare for CAT?

Tricks to prepare - CAT Irrational Numbers


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  • It is one of the most important topics in the CAT exam. Log CAT questions deal with the basic logarithm concept i.e Logarithms are the opposite function of exponents.

  • Do practice a lot, as practicing is very important to solve CAT logarithm questions quickly and accurately. Maintain a diary to note important formulas for log questions and revise them in your free time to increase your efficiency and accuracy. Attempt BYJU’S Exam Prep CAT online test series and analyse your preparation level

  • If you think technically, then the answer is yes as graph questions of Log are part of Log CAT questions. But these are not too important. So, complete the other scoring part of the quants syllabus for the  CAT Exam since there are not a lot of questions pertaining to Log graphs usually.

  • In order to prepare best for CAT Logarithm questions, the aspirants can follow the below-listed books:

    • How to prepare for Quantitative Aptitude for CAT by Arun Sharma
    • The Pearson Guide to Quantitative Aptitude and Data Interpretation by Nishit Sinha
    • Quantum CAT bySarvesh Verma
    • NCERT Mathematics books ( classes 9, 10, 11, and 12)
  • If you check any CAT Previous Year’s Paper, then you will find that the number of CAT Logarithm Questions varies between 2-3. However, only 1 question was asked last year in this section

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