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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
    Choice A
    6-1/6

  2. CAT Exponents and Logarithms: Simple

    log9 (3log2 (1 + log3 (1 + 2log2x))) = \\frac{1}{2}\\). Find x.

    1. 4
    2. \\frac{1}{2}\\)
    3. 1
    4. 2
    Choice D
    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
    Choice C
    x can be either a positive value or a negative value

  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}\\)
    Choice D
    \\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
    Choice A
    214

  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}\\)
    Choice A
    \\frac{a + b}{2ab}\\)

  7. CAT Exponents and Logarithms: Basic identities of Logarithm

    log3x + logx3 = \\frac{17}{4}\\). Find x.

    1. 34
    2. 31/8
    3. 31/4
    4. 31/3
    Choice C
    31/4

  8. CAT Exponents and Logarithms: Basic identities of Logarithm

    logxy + logyx2 = 3. Find logxy3.

    1. 4
    2. 3
    3. 31/2
    4. 31/16
    Choice B
    3

  9. 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
    Choice B
    48

  10. 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
    Choice D
    11

  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 + log216y1/2z = 6. Find the value of x + y + z.

    1. 189
    2. 190
    3. 199
    4. 201
    Choice A
    189

  12. 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
    Choice D
    none of these

  13. 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
    Choice A
    7


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