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Arithmetic Aptitude :: Logarithm

  1. Which of the following statements is not correct?

  2. A.

    log10 10 = 1

    B.

    log (2 + 3) = log (2 x 3)

    C.

    log10 1 = 0

    D.
    log (1 + 2 + 3) = log 1 + log 2 + log 3

  3. If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:

  4. A.

    2.870

    B.

    2.967

    C.

    3.876

    D.

    3.912


  5. \( \frac { log\sqrt{8} } { log8 } \)is equal to:

  6. A.

    \(\)\(\frac { 1 } { \sqrt{8} } \)

    B.

    \( \frac { 1 } { 4 } \)

    C.

    \(\frac { 1 } {4 } \)

    D.

    \( \frac { 1 } { 8} \)


  7. If log 27 = 1.431, then the value of log 9 is:

  8. A.

    0.934

    B.

    0.945

    C.

    0.954

    D.

    0.958


  9. If log\( \frac {a} {b } \)+log\( \frac {b} {a } \)=log (a + b), then

  10. A.

    a + b = 1

    B.

    a - b = 1

    C.

    a = b

    D.

    a2 - b2 = 1


  11. If log10 7 = a, then log10\([ \frac { 1 } { 70 }] \)is equal to:

  12. A.

    - (1 + a)

    B.

    (1 + a)-1

    C.

    \(\frac { a } { 10 }\)

    D.

    \(\frac { 1 } { 10a }\)


  13. If log10 2 = 0.3010, then log2 10 is equal to:

  14. A.

    \( \frac { 699 } { 301 } \)

    B.

    \( \frac { 1000 } { 301 } \)

    C.

    0.3010

    D.

    0.6990


  15. If log10 2 = 0.3010, the value of log10 80 is:

  16. A.

    1.6020

    B.

    1.9030

    C.

    3.9030

    D.

    None of these


  17. If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:

  18. A.

    1

    B.

    3

    C.

    5

    D.

    10


  19. The value of\([\frac { 1 } { log^360 }+€‹€‹\)\([\frac { 1 } { log^460 }+€‹€‹\)\([\frac { 1 } { log^560 }]\)is

     

  20. A.

    0

    B.

    1

    C.

    5

    D.

    60


  21. If log 2 = 0.30103, the number of digits in 264 is:

  22. A.

    18

    B.

    19

    C.

    20

    D.

    21


  23. If logx\([\frac { 9 } {16 } ]=\)\(-[\frac { 1 } {2 } ],\)then x is equal to:

     

     

  24. A.

    \(-\frac { 3} {4 } \)

    B.

    \(\frac { 3} {4 } \)

    C.

    \( \frac {8 1 } { 256 }\)

    D.

    \( \frac {256 } { 81}\)


  25. If ax = by, then:

  26. A.

    log\( \frac {a } {b } \)=\( \frac {X } {Y } \)

    B.

    \( \frac { loga } { logb }\)=\( \frac {X } {Y } \)

    C.

    \( \frac { loga } { logb }\)=\( \frac {Y } {X } \)

    D.

    None of these


  27.  

    If logx y = 100 and log2 x = 10, then the value of y is:

  28. A.

    210

    B.

    2100

    C.

    21000

    D.

    210000


  29. The value of log2 16 is:

  30. A.

    \(\frac { 1 } { 8 } \)

    B.

    4

    C.

    8

    D.

    16