Logarithm Questions

Laws of Logarithms Questions

Q 1. If log₁₀ 5 = x, then log₂ 1250 is
A. 3 + 1/x
B. 3 – 1/x
C. 2 + 1/x
D. 2 – 1/x

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Answer:-A. 3 + 1/x

Q 2. The number log₂ 7 is
A. An integer
B. A rational number
C. An irrational number
D. A prime number

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Answer:-C. An irrational number

Q 3. Let x > 1, y > 1, z > 1 and x² = yz. The value of  is
A. 8
B. 9
C. 10
D. 25

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Answer:-B. 9

Q 4. The number log₂ 7 is
A. An integer
B. A rational number
C. An irrational number
D. A prime number

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Answer:-C. An irrational number

Q 5. log ab – log | b | =
A. log a
B. log | a |
C. –log a
D. None of these

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Answer:-B. log | a |

Q 6. If x² + y² = 6xy, then 2log (x – y) is
A. log x +  log y + 3 log 2
B. log x +  log y + 2 log 2
C. log x +  log y + 4 log 2
D. log x +  log y + 3 log 5

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Answer:-B. log x +  log y + 2 log 2

Q 7. If a = log₂₄ 12, b = log₂₆ 24 and c = log₄₈ 36 then 1+abc is equal to
A. 2ab
B. 2ac
C. 2bc
D. 0

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Answer:-C. 2bc

Q 8. If log 3 = 0.4771, then the number of digits in 3⁴⁸ is
A. 18
B. 22
C. 23
D. 29

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Answer:-C. 23

Q 9. If a^x = b, b^y = c, c^z = a, then value of xyz is
A. 0
B. 1
C. 2
D. 3

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Answer:-B. 1

Q 10.  If log₁₀ 2 = 0.3010, then the value of log₈ 25 is
A. 1.020
B. 1.462
C. 1.548
D. 3.681

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Answer:-C. 1.548

Q 11.  If log₁₀ 2 = 0.30103, log₁₀ 3 = 0.47712, the number of digits in 3¹² x 2⁸ is
A. 7
B. 8
C. 9
D. 10

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Answer:-C. 9

Q 12. If log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) + 1. Then the value of ‘x’ is
A. 3
B. 4
C. 5
D. 6

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Answer:-A. 3

Q 13. If x = log₅ (1000) and y = log₇ (2058) then
A. x > y
B. x < y
C. x = y
D. None of these

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Answer:-A. x > y

Q 14. If log (10x + 5) – log(x – 4) = 2, then the value of ‘x’ is
A. 2.5
B. 3.5
C. 4.5
D. 5.5

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Answer:-C. 4.5

Q 15. log₄ 18 is
A. A rational number
B. An irrational number
C. A prime number
D. None of these

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Answer:-B. An irrational number

Q16. If a = 1 + log₁₀ 2 – log₁₀ 5, b = 2 log₁₀ 3  and  c = log₁₀ m – log₁₀ 5, then the value of ‘m’ if a + b = 2c is
A. 15
B. 16
C. 20
D. 30

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Answer:-D. 30

Q 17. If a, b, c are distinct positive numbers, each different from 1,  such that [log_b a log_c a – log_a a] + [log_a b log_cb – log_b b] + [log_a c log_b c – log_c c] = 0, then abc =
A. 1
B. 2
C. 3
D. None of these

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Answer:-A. 1

Q 18. If log2 = 0.3010, then the value of log 250 is
A. 2.3980
B. 1.6811
C. 2.4896
D. 1.5841

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Answer:-A. 2.3980

Q 19. If log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) +1, then the value of x is
A. 3
B. 5
C. 6
D. 2

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Answer:-D. 2

Q 20. If x = log_b a, y = log_c b, z = log_a c, then xyz is
A. 0
B. 1
C. 3
D. None of these

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Answer:-B. 1

Q 21. If log 303 = x and log 305 = y, then log 308 is
A. 3(1– x – y)
B. 3(1 + x – y)
C. 3(1 + x + y)
D. 3(x + y)

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Answer:-A. 3(1– x – y)

Q 22.The number of  real values of the parameter k for which (log₁₆ x)² – log₁₆ x + log₁₆ k = 0 with real coefficients will have exactly one solution is
A. 1
B. 15
C. 44
D. None of these

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Answer:-A. 1

Q 23. The value of x in  = 9^{2x – 2} is
A. 8/7
B. 12/8
C. 15/4
D. 16/7

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Answer:-A. 8/7

Q 24. If log₁₀ ³ = 0.477, the number of digits in 3⁴⁰ is
A. 18
B. 19
C. 20
D. 21

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Answer:-C. 20

Q 25. If log₁₀ 3 = 0.477, then the number of digits in 3⁴⁰ is
A. 19
B. 20
C. 21
D. 22

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Answer:-B. 20

Q 26. If 3^x – 3^{x – 1} = 6, then x^x is equal to
A. 2
B. 4
C. 9
D. None of these

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Answer:-B. 4

Q 27. If log 3 = 0.4771, then the number of digits in 3⁴⁸ is
A. 18
B. 22
C. 23
D. 49

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Answer:-C. 23

Q 28. The value of log₃ 4 log₄ 5 log₅ 6 log₆ 7log₇ 8log₈ 9 is
A. 1
B. 2
C. 3
D. 4

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Answer:-B. 2

Q 29. If log₁₀ x = 2log₁₀ (5.87) – 1/2 log₁₀ (0.839). Then the value of ‘x’ is
A. 21.6
B. 32.3
C. 32.8
D. 37.6

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Answer:-D. 37.6

Q 30. If log 10x = y, then log₁₀₀₀ x² is equal to
A. y + 2
B. 2y
C. 3y/2
D. 2y/3

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Answer:-D. 2y/3

Q 31. If log_e2 . log_y625 = log₁₀16 . log_e10, then the value of y is
A. 3
B. 4
C. 5
D. None

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Answer:-C. 5

Q 32.If x = 27, y = log 34, then xy = ___
A. 64
B. 66
C. 67
D. 71

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Answer:-A. 64

Q 33. If log₃₀ 3 = x and log₃₀ 5 = y, then log₃₀ 8 is
A. 3(1– x – y)
B. 3(1 + x – y)
C. 3(1 + x + y)
D. 3(x + y)

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Answer:-A. 3(1– x – y)

Q 34.  If  x = log ba, y = log cb, z = log ac, then xyz is
A. 0
B. 1
C. 3
D. None

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Answer:-B. 1

Q 35. If log 102 = 0.3010, then the value of log 825 is
A. 1.548
B. 2.462
C. 3.481
D. 6.020

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Answer:-A. 1.548

Q 36. If log5 a . loga x = 2, then x is equal to
A. 20
B. 25
C. 125
D. 160

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Answer:-B. 25

Q 37. If log (10x + 5) – log(x – 4) = 2, then the value of ‘x’ is
A. 3.5
B. 2.5
C. 4.5
D. 5.5

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Answer:-C. 4.5

Q 38. If x = 27, y = log₃ 4, then x^y = __
A. 6
B. 16
C. 46
D. 64

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Answer:-D. 64

Q 39. If a = 1 + log102 – log 105, b = 2 log103  and  c = log10m – log105, then the value of ‘m’ if a + b = 2c is
A. 25
B. 30
C. 36
D. 40

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Answer:-B. 30

Q 40. If x = log_b a, y = log_c b, z = log_a c, then xyz is
A. 0
B. 1
C. 3
D. None

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Answer:-B. 1

Q 41. If log 2 = 0.3010, then the value of log 250 is
A. 2.3980
B. 1.6811
C. 2.4896
D. 1.5841

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Answer:-A. 2.3980

Q 42. If 7^x+1 – 7^x–1 = 48. Then the value of ‘x’ is
A. 0
B. 1
C. 2
D. 3

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Answer:-B. 1

Q 43. If loge2 . logy625=log1016 . loge10, then the value of y is
A. 4
B. 5
C. 3
D. None

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Answer:-B. 5