Logarithms or logs is one of the easiest topics to cover for the Quantitative Aptitude section in any MBA entrance exam. It assesses a candidate with his/her ability to calculate the log of a given number n as an exponent to which another fixed number, the base b, must be raised, to produce that number n.

A candidate can easily expect 2-3 questions based on logarithm in CAT and other MBA exams such as NMAT, XAT, SNAP, etc.

Exams which use contain this topic:

CAT – Log questions in CAT may range from very easy to very high level of difficulty. You may expect 2-3 questions from this topic. CAT has been consistently assessing candidates on Logarithms and exponents

YearNo of QuestionsLevel of Difficulty




Slot 11Easy
Slot 22Easy to moderate




Slot 13Moderate
Slot 23Moderate to High

NMAT – The Log questions in NMAT usually range from easy to moderate and are a must attempt. One must not miss out on these questions.


YearNo of QuestionsLevel of Difficulty
20192Easy to Moderate


List of basic concepts of Logs:

Logarithm questions are generally direct, but the level of difficulty may be increased by adding the concept of the number of digits.

Listed below are a few concepts that may help you gain insight into the type of questions asked:

If ax  = N , then, x = log of N to the base a and x = logaN . In other words, it represents the power to which a number must be raised.

Suppose we are asked the result if ‘x’ is multiplied by itself ‘y’ times; then your answer would be x = x*x*x*…. y (times). This can also be written as x^y. This is also known as ‘x raised to the power of y’

The log of a number comprises 2 parts:

  1. The integral part is called Characteristic
  2. The decimal part is called Mantissa

For example, Log 27 = 3 Log 3 = 3*0.4771 = 1.4313


In this case, the characteristic is 1 and the mantissa is 0.4313

Important formulae to remember:

  • logxx = 1
  • logx1 = 0
  • logxab = b logx a
  • logx(mn) = logx m + logx n
  • logxax = a
  • logxm = (logy n) x (loga n)
  • logx(mn) = logx m + logx n
  • logx(m/n) = logx m – logx n

Key points to note:

  1. The characteristic of a number greater than unity for a common base is positive and is 1 less than the number of digits in an integral part. For example, the Characteristic of log 1000 = 3 which is 1 less than the number of digits in 1000.
  2. For a number between 0 and 1, the characteristic is negative, and its magnitude is 1 more than the number of zeros after the decimal point. For example: Characteristic of log 0.001 = -3.
  3. log( x – y ) ≠ logx – logy
  4. log( x + y ) ≠ logx + logy

Some Questions from Previous Papers

CAT 2019 Slot 1:  Let x and y be positive real numbers such that log5 (x + y) + log5 (x y) = 3, and log2 y log2 x = 1 log2 3. Then xy equals 

1. 150 

2. 100 

3. 25 

4. 250


Ans. Given, log(base5) (x + y) + log(base5) (x − y) = 3

Or log(base5) (x + y)*(x-y) =3

Or x^2 –y^2 = 5^3 = 125————-1)

log(base2) y − log(base2) x = 1 − log(base2) 3= log(base2) 2 – log(base2) 3

log(base2) y/x = log(base2) 2/3

y/x = 2/3

y = 2x/3

from eq 1) x^2 – (2x/3)^2 = 125

x^2 – (4x^2/9) = 125

5x^2 = 125*9 or x^2 = 225

x = 15

y= 2x/3 = 30/3 = 10


xy = 15*10 =150

Details on This Page

Words From Our Students

Nihar Mehta
Nihar Mehta
Calls from IIMs, SPJIMR & MDI
Read More
I joined the classroom coaching programme at MBA Pathshala for my CAT preparation. Since the very beginning, Abhijit Sir & Haider Sir guided me in terms of the strategy & the approach required in order to fare well in the exam. They not only stressed on the academics but also pushed me to build my profile aligned with my interests. Post CAT, they gave me ample practice for my GD & PI preparations with sufficient number of mock interviews & regular feedback for improvement. I managed to get calls from IIMs, SPJIMR & MDI. A huge part in this goes to the team at MBAP and I am cannot thank them enough for their contribution.
Ishan Rathod
Ishan Rathod
Calls from IIM I, S, and all New And Baby IIM's.
Read More
MBAP is great place to preparing for MBA-CET,CAT,CMAT and faculty are unbeatable. They are very helpful best part is they give personal attention to each and every students. Most of faculty...who are alumni of IIM and JBIMS. There is more one to one interaction which helped me get better as the exams approached and helped me get calls from IIM I, S, and all New And Baby IIM's. The interview sessions proved to be of great learning helped me convert IIM S
Sanskriti Reja
Sanskriti Reja
Calls from IIMs, XLRI, XIMB
Read More
MBA Pathshala was my first choice for MBA coaching and I'm happy that joined it. The faculty here is great.. they are really good in what they do. They supported me and motivated me during my journey of clearingthe entrances. They are always available for the doubts, extra lectures. they helped me get through my GD-PIs too after the exams. I am thankful to MBAP for helping me to crack CAT and other entrance exams. I got calls from XLRI, XIMB, IIMs, among others. I have converted colleges like KJ Somaiya, TAPMI, IIM Sambalpur, IIM Sirmaur.
Parth Kanakia
Parth Kanakia
Converted SPJIMR
Read More
I joined MBAP for GD, WAT & PI preparation. Received very good training from Abhijit Singh, Haider and other MBAP faculty. Starting from very basics, good knowledge was provided. Mock interviews were conducted on regular basis. I converted SPJIMR and I would definitely recommend students to join MBAP.
Ronit jaiswal
Ronit jaiswal
Calls from IIM-A/B/C & SNAP 98.12%ile
Read More
I wanted to join a coaching where I can get personalised attention and competitive environment. I got both in MBAP. All the preparation was so rigorous that I eventually started giving my best. They conducted mock interviews/GD/WAT with anonymous panels and trust me it was such a confidence booster. I got a call from SCMHRD (SNAP-98.12) However I always wanted to go for IIM and Abhijeet sir felt that and he convinced me to try again and aim for IIM-A/B/C. Here I am back under his mentorship again. In short give your best and they will bring the best out of you. P.S- I'm a working individual. If I can do it then anybody can. Thank you for being such a great mentors.
Maitreya Khanapurkar
Maitreya Khanapurkar
Calls From IIMs
Read More
Best learning experience.Faculties are good and you will get a good support from them till you get admission into a B-School.The shortcut techniques taught will be of great help for you. Doubts will be solved anytime you want. If planning for CAT CET or any entrance exam go for MBA Pathshala. It was of tutors at MBAP I received a call from IMT Ghaziabad.
Yash Dandavate
GMAT Score - 660
Read More
I joined MBAP for GMAT prep and my experience with them was really amazing, from the first day itself the faculties gave personal attention to each student and made sure each student had their own personalised GMAT and CAT prep plans. The Verbal faculty Rohan Kulkarni Sir was amazing, I was very weak in English and verbal section, but through his guidance I scored a V38 (85th percentile) in my GMAT exam. The Quant faculties Abhijeet and Haider Sir helped me develop strategies and short cuts to approach GMAT problems and we're always available for my doubts. Overall it was a great experience and I would reccomend MBAP to everyone for GMAT and CAT prep

CAT 2019 Slot 2:  If x is a real number, then is a real number if and only if 

1. 1≤x≤2 

2. -3≤x≤3 

3. -1≤x≤3 

4. 1≤x≤3

Ans. As we know that any value under square root must be greater than 0. So Log(base e) 4x-x^2/3 ≥ 0 

So, 4x-x^2/3≥ 1 

x^2-4x +3 ≤ 0 


On solving, we get S belongs to [1,3]


CAT 2019 Slot 2: The real root of the equation 2 6x + 2 3x+2 – 21 = 0 is 

1. log(base2)3 / 2 

2. log(base2)9 

3. log(base2)27 

4. log(base2)7 / 3

Ans. Let 2^(3x) = k 

So given equation 2^6x + 2^(3x+2) – 21 =0 

Or (2^3x)^2 + 4*2^3x -21 =0 

Or k^2 + 4k -21 =0 

(k+7)*(k-3) =0 

k = -4 or 3 

k= -4 is not possible 

so k =3 

or 2^3x = 3 

taking log of both sides 3x * log 2 = log 3 

3x = log 3 / log 2 

3x = log(base2)⁡3 

Or x = (log(base2⁡)3) /3 

Option a) (log(base2)⁡3) /3


XAT: Find the value of log10 10 + log10 10 2 + ….. + log10 10 n

1. n^2 + 1

2. n^2 − 1

3. (n^2 +n)/2 n(n+1)/3

4. (n^2 +n)/2

log10 10 + log10 10 2 + ….. + log10 10 n

Since loga = 1

log10 10 + log10 10 2 + ….. + log10 10 n=1+2+…n

n(n+1) 2 (n +n)

D is the correct answer.


How to deal with that topic preparation

Preparing for Logarithm will require a basic understanding of the key concepts and formulae along with patience and a knack for learning. Here are some Level-wise preparatory guidelines to follow:

Level – 1

  • Learn the basic concepts of logarithm thoroughly.
  • Learn Speed calculation: For an effective and quick calculation, be thorough with tables till 20, memorize squares till 30, and cubes till 15.
  • Memorize the properties of the log.
  • Practice beginner-level questions.

Level – 2

  • Move on to more complex problems, attempt beginner and intermediate level mock on concepts of Logarithm.
  • Solve previous year CAT questions on Logs and time yourself. Do not get stuck on one question and try to solve easy questions first.
  • Keep attempting mocks to check your performance.
  • Topic-wise mocks, provided by MBAP, can be utilized to enhance your performance.

Level – 3

  • For advanced level preparation, start practicing questions from the book – How to Prepare for Quantitative Aptitude for the CAT, authored by Arun Sharma.
  • Questions in Arun Sharma are categorized into Level of Difficulty (LOD), based upon your preparation level, start attempting 3 or 4 questions daily.