# CAT Questions | CAT Arithmetic

###### CAT Quantitative Aptitude | CAT Exponents and Logarithms

CAT Exponents and Logarithms Questions are one of the most commonly tested topics in CAT exam. Questions from Exponents and Logarithms have appeared consistently in the CAT exam for the last several years. Questions from Exponents and Logarithms range from very easy to very hard. The basic concept is very easy, learn the concepts and practice a wide range of CAT Questions from 2IIM. One can usually expect 2-3 questions from Logarithms and Exponents in the CAT exam. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

1. #### CAT Exponents and Logarithms: Inequalities

If log2X + log4X = log0.25√6 and x > 0, then x is

1. 6-1/6
2. 61/6
3. 3-1/3
4. 61/3

log9 (3log2 (1 + log3 (1 + 2log2x))) = $$frac{1}{2}\\$. Find x. 1. 4 2. $\frac{1}{2}\\$ 3. 1 4. 2 3. #### CAT Exponents and Logarithms: Quadratic Equations If 22x+4 – 17 × 2x+1 = –4, then which of the following is true? 1. x is a positive value 2. x is a negative value 3. x can be either a positive value or a negative value 4. None of these 4. #### CAT Exponents and Logarithms: Algebra If log1227 = a, log916 = b, find log8108. 1. $\frac{2$a + 3$}{3b}$ 2. $\frac{2$a + 3$}{3a}$ 3. $\frac{2$b + 3$}{3a}$ 4. $\frac{2$b + 3$}{3b}$ 5. #### CAT Exponents and Logarithms: Inequalities $\frac{log_3$x-3$}{log_3(x-5)}$ < 0. If a, b are integers such that x = a, and x = b satisfy this inequation, find the maximum possible value of a – b. 1. 214 2. 216 3. 200 4. 203 6. #### CAT Exponents and Logarithms: Different bases log5x = a$This should be read as log X to the base 5 equals a) log20x = b. What is logx10?

1. $$frac{a + b}{2ab}\\$ 2.$a + b) * 2ab
3. $$frac{2ab}{a + b}\\$ 4. $\frac{a + b}{2}\\$ 7. #### CAT Exponents and Logarithms: Basic identities of Logarithm log3x + logx3 = $\frac{17}{4}\\$. Find the value of x. 1. 34 2. 31/4 3. 34 or 31/4 4. 31/3 8. 34 or 31/4 • #### CAT Exponents and Logarithms: Basic identities of Logarithm logxy + logyx2 = 3. Find logxy3. 1. 4 2. 3 3. 31/2 4. 31/16 • #### CAT Exponents and Logarithms: Basic identities of Logarithm If log2 4 * log4 8 * log8 16 * ……………nth term = 49, what is the value of n? 1. 49 2. 48 3. 34 4. 24 • #### CAT Exponents and Logarithms: Basic identities of Logarithm If 33 + 6 + 9 + ……… 3x =$0.$$overline{037}\\$)-66, what is the value of x? 1. 3 2. 6 3. 7 4. 11 • #### CAT Exponents and Logarithms: Basic identities of Logarithm x, y, z are 3 integers in a geometric sequence such that y - x is a perfect cube. Given, log36x2 + log6√y + 3log216y1/2z = 6. Find the value of x + y + z. 1. 189 2. 190 3. 199 4. 201 • #### CAT Exponents and Logarithms: Basic identities of Logarithm 10log$3 - 10logy) = log2(9 - 2y), Solve for y.

1. 0
2. 3
3. 0 and 3
4. none of these

• #### CAT Exponents and Logarithms: Value of x

46+12+18+24+…+6x = (0.0625)-84, what is the value of x?

1. 7
2. 6
3. 9
4. 12

• ##### The following questions are from IPMAT Rohtak and Indore sample papers. If you want to take these questions as a mock please click below.

IPMAT Rohtak Sample Paper Mock
IPMAT Indore Sample Paper Mock

Please note that the explanation button will take you to the IPMAT solution page.

• #### IPMAT 2020 Sample Paper - IPM Rohtak Quants,Exponents and Logarithms

Simplification: $25^{$2.7)} $times 5^{$4.2)} $div 5^{$5.4)} = ?$ 1. 54 2. 5$3.2)
3. 5(4.1)
4. 5(4.2)

Suppose that a, b, and c are real numbers greater than 1. Then the value of $$frac{1}{1+\log _{a^{2} b} \frac{c}{a}}+\frac{1}{1+\log _{b^{2} c} \frac{a}{b}}+\frac{1}{1+\log _{c^{2} a} \frac{b}{c}}\\$ is • #### IPMAT 2019 Question Paper - IPM Indore Quants,Exponents and Logarithms The value of $\log _{3} 30^{-1} + \log _{4} 900^{-1} + \log _{5} 30^{-1}\\$ is 1. 0.5 2. 30 3. 2 4. 1 • #### IPMAT 2019 Question Paper - IPM Indore Quants,Exponents and Logarithms The inequality $\log _{a}{f$x$} < $log _{a}{g$x)}$ implies that 1. f$x) > g(x) > 0 for 0 < a < 1 and g(x) > f(x) > 0 for a > 1
2. g(x) > f(x) > 0 for 0 < a < 1 and f(x) > g(x) > 0 for a > 1
3. f(x) > g(x) > 0 for a > 0
4. g(x) > f(x) > 0 for a > 0

• The Questions that follow, are from actual CAT papers. If you wish to take them separately or plan to solve actual CAT papers at a later point in time, It would be a good idea to stop here.

1. #### CAT 2020 Question Paper Slot 3 - Exponents & Powers

If x1 = -1 and xm = xm + 1 + (m + 1) for every positive integer m, then x100 equals

1. -5050
2. -5051
3. -5150
4. -5151

7. #### CAT 2020 Question Paper Slot 1 - Exponents & Powers

The number of real-valued solutions of the equation 2x + 2-x = 2 - (x - 2)2 is

1. infinite
2. 0
3. 1
4. 2

8. #### CAT 2020 Question Paper Slot 1 - Exponents & Powers

If x = (4096)7+4√3, then which of the following equals 64?

1. $$frac{x^{7/2}}{x^{4/√3}}$ 2. $\frac{x^{7}}{x^{4√3}}$ 3. $\frac{x^{7/2}}{x^{2√3}}$ 4. $\frac{x^{7}}{x^{2√3}}$ 9. #### CAT 2020 Question Paper Slot 1 - Exponents & Powers If y is a negative number such that 2y2log35 = 5log23, then y equals 1. log$1/3)
2. log(1/5)
3. −log(1/3)
4. −log(1/5)

10. #### CAT 2019 Question Paper Slot 2 - Logarithms

The real root of the equation 26x + 23x+2 - 21 = 0 is

1. -16
2. -24
3. -12
4. -20

3. #### CAT 2019 Question Paper Slot 1 - Logarithms

Let x and y be positive real numbers such that log5(x + y) + log5(x - y) = 3, and log2y - log2x = 1 - log23. Then xy equals

1. 25
2. 150
3. 250
4. 100
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4. #### CAT 2018 Question Paper Slot 2 - Logarithm

If p3 = q4 = r5 = s6, then the value of logs (pqr) is equal to

1. 32
2. 59
3. 67
4. 40

10. #### CAT 2017 Question Paper Slot 2 - Exponents & Logarithms

If x is a real number such that log35 = log5(2 + x), then which of the following is true?

1. 0 < x < 3
2. 23 < x < 30
3. x > 30
4. 3 < x < 23

1. #### CAT 2017 Question Paper Slot 1 - Exponents & Logarithms

Suppose, log3x = log12y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log6G is equal to:

1. √a
2. 2a
3. $$frac{a}{2}$ 4. a 2. #### CAT 2017 Question Paper Slot 1 - Exponents & Logarithms The value of log0.008√5 + log√381 – 7 is equal to: 1. $\frac{1}{3}$ 2. $\frac{2}{3}$ 3. $\frac{5}{6}$ 4. $\frac{7}{6}$ 3. #### CAT 2017 Question Paper Slot 1 - Exponents & Logarithms If 92x – 1 – 81x-1 = 1944, then x is 1. 3 2. $\frac{9}{4}$ 3. $\frac{4}{9}$ 4. $\frac{1}{3}$ ###### 🏏 CAT 2021 could be your Gabba Victory! Fabulous 5,000 off on online courses. Valid until 20th Jan ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2021Enroll at 49,000/- 44,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Preparation Online | CAT Arithmetic Videos On YouTube #### Other useful sources for Arithmetic Question | Logarithms and Exponents Sample Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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