CAT Practice : Exponents and Logarithms

You are here: Home  CAT Questionbank   CAT Quant  Exponents and Logarithms
The following topics are covered in the CAT quant section from Arithmetic in Exponents and Logarithms. Detailed explanatory answers, solution videos and slide decks are also provided.
  1. Logarithm - Inequalities

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

    1. 6-1/6
    2. 61/6
    3. 3-1/3
    4. 61/3
    • Correct AnswerChoice (A).
      6-1/6
      Correct answer
    • Explanatory Answer
    • Logarithm - Inequalities
    • Medium
  2. Logarithm - Simple

    log9 (3log2 (1 + log3 (1 + 2log2x))) = . Find x.

    1. 4
    2. 1
    3. 2
  3. Logartihm - 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
    • Correct AnswerChoice (C).
      x can be either a positive value or a negative value
      Correct answer
    • Explanatory Answer
    • Exponents - Quadratic Equations
    • Easy
  4. Logartihm - Algebra

    If log1227 = a, log916 = b, find log8108.

    • Correct AnswerChoice (D).
      Correct answer
    • Explanatory Answer
    • Logarithm manipulation
    • Hard
  5. Logarithm - 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.

    1. 214
    2. 216
    3. 200
    4. 203
    • Correct AnswerChoice (A).
      214
      Correct answer
    • Explanatory Answer
    • Logarithm - Inequalities
    • Hard
  6. Logarithms - Different bases

    log5x = a (This should be read as log X to the base 5 equals a) log20x = b. What is logx10?

    1. (a + b) * 2ab
    • Correct AnswerChoice (A).
      Correct answer
    • Explanatory Answer
    • Logarithm - Algebra
    • Medium
  7. Basic identities of Logarithm

    Find x.

    • Correct AnswerChoice (C).
      Correct answer
    • Explanatory Answer
    • Basic identities of Logarithm
    • Medium
  8. Basic identities of Logarithm

    Find

    1. 4
    2. 3


    • Correct AnswerChoice (B).
      3
      Correct answer
    • Explanatory Answer
    • Basic identities of Logarithm
    • Medium
  9. 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
    • Correct AnswerChoice (B).
      48
      Correct answer
    • Explanatory Answer
    • Basic identities of Logarithm
    • Hard
  10. Basic identities of Logarithm

    If 33+6+9+……….x terms = (0.)-66 and (x > 70),
    What is the value of x?

    1. 3
    2. 6
    3. 7
    4. 11
    • Correct AnswerChoice (D).
      11
      Correct answer
    • Explanatory Answer
    • Basic identities of Logarithm
    • Hard
  11. 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
    • Correct AnswerChoice (A).
      189
      Correct answer
    • Explanatory Answer
    • Basic identities of Logarithm
    • Hard
  12. 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
    • Correct AnswerChoice (D).
      none of these
      Correct answer
    • Explanatory Answer
    • Basic identities of Logarithm
    • Medium
  13. 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

Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.


Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play