CAT Questions | CAT Arithmetic Questions | Logarithms and Exponents

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 = log_0.25?6 and x > 0, then x is
   
   A. 6^-1/6
   
   B. 6^1/6
   
   C. 3^-1/3
   
   D. 6^1/3
   
   

   Correct Answer

   Choice A
   6^-1/6

   Explanation
   

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2. CAT Exponents and Logarithms: Simple

   log₉ (3log₂ (1 + log₃ (1 + 2log₂x))) = . Find x.
   
   A. 4
   
   B.
   
   C. 1
   
   D. 2
   
   

   Correct Answer

   Choice D
   2

   Explanation
   

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3. CAT Exponents and Logarithms: Quadratic Equations

   If 2^2x+4 – 17 × 2^x+1 = –4, then which of the following is true?
   
   A. x is a positive value
   
   B. x is a negative value
   
   C. x can be either a positive value or a negative value
   
   D. None of these
   
   

   Correct Answer

   Choice C
   x can be either a positive value or a negative value

   Explanation
   

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4. CAT Exponents and Logarithms: Algebra

   If log₁₂27 = a, log₉16 = b, find log₈108.
   
   A.
   
   B.
   
   C.
   
   D.
   
   

   Correct Answer

   Choice D
   ^{2(b + 3)}⁄_3b

   Explanation
   

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5. CAT Exponents and Logarithms: Inequalities

   < 0. If a, b are integers such that x = a, and x = b satisfy this inequation, find the maximum possible value of a – b.
   
   A. 214
   
   B. 216
   
   C. 200
   
   D. 203
   
   

   Correct Answer

   Choice A
   214

   Explanation

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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 log_x10?
   
   A.
   
   B. (a + b) × 2ab
   
   C.
   
   D.
   
   

   Correct Answer

   Choice A
   ^{(a + b)}⁄_(2ab)

   Explanation

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7. CAT Exponents and Logarithms: Basic identities of Logarithm

   log₃x + log_x3 = . Find x.
   
   A. 3⁴
   
   B. 3^1/8
   
   C. 3^1/4
   
   D. 3^1/3
   
   

   Correct Answer

   Choice C
   3^1/4

   Explanation

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8. CAT Exponents and Logarithms: Basic identities of Logarithm

   log_xy + log_yx² = 3. Find log_xy³.
   
   A. 4
   
   B. 3
   
   C. 3^1/2
   
   D. 3^1/16
   
   

   Correct Answer

   Choice B
   3

   Explanation

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9. CAT Exponents and Logarithms: Basic identities of Logarithm

   If log₂ 4 × log₄ 8 × log₈ 16 × ............ n^th term = 49, what is the value of n?
   
   A. 49
   
   B. 48
   
   C. 34
   
   D. 24
   
   

   Correct Answer

   Choice B
   48

   Explanation
   

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10. CAT Exponents and Logarithms: Basic identities of Logarithm

    If 3^{3 + 6 + 9 + ......... 3x} = (0.037)^-66, what is the value of x?
    
    A. 3
    
    B. 6
    
    C. 7
    
    D. 11
    
    

    Correct Answer

    Choice D
    11

    Explanation
    

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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 + log₂₁₆y^1/2z = 6. Find the value of x + y + z.
    
    A. 189
    
    B. 190
    
    C. 199
    
    D. 201
    
    

    Correct Answer

    Choice A
    189

    Explanation
    

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12. CAT Exponents and Logarithms: Basic identities of Logarithm

    10^{log(3 - 10logy)} = log₂(9 - 2^y), Solve for y.
    
    A. 0
    
    B. 3
    
    C. 0 and 3
    
    D. None of these
    
    

    Correct Answer

    Choice D
    None of these

    Explanation
    

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13. CAT Exponents and Logarithms: Value of x

    4^{6+12+18+24+…+6x} = (0.0625)^-84, what is the value of x?
    
    A. 7
    
    B. 6
    
    C. 9
    
    D. 12
    
    

    Correct Answer

    Choice A
    7

    Explanation
    

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