Logarithm Questions

Laws of Logarithms Questions:

Ques. 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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Ques. The number log₂ 7 is
(a) An integer
(b) A rational number
(c) An irrational number
(d) A prime number
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Ques. Let x > 1, y > 1, z > 1 and x² = yz. The value of  is
(a) 9
(b) 8
(c) 10
(d) 25
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Ques. The number log₂ 7 is
(a) An integer
(b) A rational number
(c) An irrational number
(d) A prime number
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Ques. log ab – log | b | =
(a) log a
(b) log | a |
(c) –log a
(d) None of these
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Ques. 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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Ques. 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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Ques. If log 3 = 0.4771, then the number of digits in 3⁴⁸ is
(a) 48
(b) 22
(c) 23
(d) 49
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Ques. 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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Ques. If log₁₀ 2 = 0.3010, then the value of log₈ 25 is
(a) 6.020
(b) 2.462
(c) 1.548
(d) 3.481
View Answer

Ques. 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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Ques. If log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) + 1. Then the value of ‘x’ is
(a) 3
(b) 6
(c) 4
(d) 5
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Ques. 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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Ques. If log (10x + 5) – log(x – 4) = 2, then the value of ‘x’ is
(a) 4.5
(b) 3.5
(c) 2.5
(d) 5.5
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Ques. log₄ 18 is
(a) A rational number
(b) An irrational number
(c) A prime number
(d) None of these
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Ques. 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) 25
(b) 36
(c) 40
(d) 30
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Ques. 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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Ques. If log2 = 0.3010, then the value of log 250 is
(a) 2.3980
(b) 1.6811
(c) 2.4896
(d) 1.5841
View Answer

Ques. If log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) +1, then the value of x is
(a) 3
(b) 5
(c) 6
(d) 2
View Answer

Ques. 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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Ques. 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)
View Answer

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Ques. 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) 2
(b) 1
(c) 4
(d) None of these
View Answer

Ques. The value of x in  = 9^{2x – 2} is
(a) 8/7
(b) 7/8
(c) 7/4
(d) 16/7
View Answer

Ques. If log₁₀ ³ = 0.477, the number of digits in 3⁴⁰ is
(a) 18
(b) 19
(c) 20
(d) 21
View Answer

Ques. If log₁₀ 3 = 0.477, then the number of digits in 3⁴⁰ is
(a) 19
(b) 20
(c) 21
(d) 22
View Answer

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Ques. If 3^x – 3^{x – 1} = 6, then x^x is equal to
(a) 2
(b) 4
(c) 9
(d) None of these
View Answer

Ques. If log 3 = 0.4771, then the number of digits in 3⁴⁸ is
(a) 48
(b) 22
(c) 23
(d) 49
View Answer

Ques. The value of log₃ 4 log₄ 5 log₅ 6 log₆ 7log₇ 8log₈ 9 is
(a) 1
(b) 2
(c) 3
(d) 4
View Answer

Ques. If log₁₀ x = 2log₁₀ (5.87) – 1/2 log₁₀ (0.839). Then the value of ‘x’ is
(a) 37.6
(b) 42.8
(c) 32.4
(d) 21.6
View Answer

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Ques. 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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Ques. If log_e2 . log_y625 = log₁₀16 . log_e10, then the value of y is
(a) 4
(b) 5
(c) 3
(d) None
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Ques. If x = 27, y = log 34, then xy = ___
(a) 64
(b) 16
(c) 4
(d) 1
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Ques. 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)
View Answer

Ques. If  x = log ba, y = log cb, z = log ac, then xyz is
(a) 0
(b) 1
(c) 3
(d) None
View Answer

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Ques. If log 102 = 0.3010, then the value of log 825 is
(a) 6.020
(b) 2.462
(c) 1.548
(d) 3.481
View Answer

Ques. If log5 a . loga x = 2, then x is equal to
(a) 125
(b) 22
(c) 25
(d) None
View Answer

Ques. If log (10x + 5) – log(x – 4) = 2, then the value of ‘x’ is
(a) 3.5
(b) 2.5
(c) 5.5
(d) 4.5
View Answer

Ques. If x = 27, y = log₃ 4, then x^y = __
(a) 64
(b) 16
(c) 4
(d) 1
View Answer

Ques. 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) 36
(c) 40
(d) 30
View Answer

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Ques. If x = log_b a, y = log_c b, z = log_a c, then xyz is
(a) 0
(b) 1
(c) 3
(d) None
View Answer

Ques. If log 2 = 0.3010, then the value of log 250 is
(a) 2.3980
(b) 1.6811
(c) 2.4896
(d) 1.5841
View Answer

Ques. If 7^x+1 – 7^x–1 = 48. Then the value of ‘x’ is
(a) 7
(b) 0
(c) 1
(d) 2
View Answer

Ques. If loge2 . logy625=log1016 . loge10, then the value of y is
(a) 4
(b) 5
(c) 3
(d) None
View Answer