# Logarithm Questions

### Laws of Logarithms Questions:

Ques. If log10 5 = x, then log2 1250 is
(a) 3 + 1/x
(b) 3 â€“ 1/x
(c) 2 + 1/x
(d) 2 â€“ 1/x

Ans. (a)

Ques. The number log2 7 is
(a) An integer
(b) A rational number
(c) An irrational number
(d) A prime number

Ans. (c)

Ques. Let x > 1, y > 1, z > 1 and x2 = yz. The value ofÂ  is
(a) 9
(b) 8
(c) 10
(d) 25

Ans. (a)

Ques. The number log2 7 is
(a) An integer
(b) A rational number
(c) An irrational number
(d) A prime number

Ans. (c)

Ques. log ab â€“ log | b | =
(a) log a
(b) log | a |
(c) â€“log a
(d) None of these

Ans. (b)

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Ques. If x2 + y2 = 6xy, then 2log (x â€“ y) is
(a) log x +Â  log y + 3 log 2
(b) log x +Â  log y + 2 log 2
(c) log x +Â  log y + 4 log 2
(d) log x +Â  log y + 3 log 5

Ans. (b)

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

Ans. (c)

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

Ans. (c)

Ques. If ax = b, by = c, cz = a, then value of xyz is
(a) 0
(b) 1
(c) 2
(d) 3

Ans. (b)

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

Ans. (c)

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

Ans. (c)

Ques. If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1. Then the value of â€˜xâ€™ is
(a) 3
(b) 6
(c) 4
(d) 5

Ans. (a)

Ques. If x = log5 (1000) and y = log7 (2058) then
(a) x > y
(b) x < y
(c) x = y
(d) None of these

Ans. (a)

Ques. If log (10x + 5) â€“ log(x â€“ 4) = 2, then the value of â€˜xâ€™ is
(a) 4.5
(b) 3.5
(c) 2.5
(d) 5.5

Ans. (a)

Ques. log4 18 is
(a) A rational number
(b) An irrational number
(c) A prime number
(d) None of these

Ans. (b)

Ques. If a = 1 + log10 2 â€“ log10 5, b = 2 log10 3Â  andÂ  c = log10 m â€“ log10 5, then the value of â€˜mâ€™ if a + b = 2c is
(a) 25
(b) 36
(c) 40
(d) 30

Ans. (d)

Ques. If a, b, c are distinct positive numbers, each different from 1,Â  such that [logb a logc a â€“ loga a] + [loga b logcb â€“ logb b] + [loga c logb c â€“ logc c] = 0, then abc =
(a) 1
(b) 2
(c) 3
(d) None of these

Ans. (a)

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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

Ans. (a)

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

Ans. (d)

Ques. If x = logb a, y = logc b, z = loga c, then xyz is
(a) 0
(b) 1
(c) 3
(d) None of these

Ans. (b)

Ques. If log 303 = x and log 305 = y, then log 308 is
(a) 3(1â€“ x â€“ y)
(b) 3(1 + x â€“ y)
(c) 3(1 + x + y)
(d) 3(x + y)

Ans. (a)

Ques. The number ofÂ  real values of the parameter k for which (log16 x)2 â€“ log16 x + log16 k = 0 with real coefficients will have exactly one solution is
(a) 2
(b) 1
(c) 4
(d) None of these

Ans. (b)

Ques. The value of x inÂ  = 92x â€“ 2 is
(a) 8/7
(b) 7/8
(c) 7/4
(d) 16/7

Ans. (a)

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

Ans. (c)

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

Ans. (b)

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Ques. If 3x â€“ 3x â€“ 1 = 6, then xx is equal to
(a) 2
(b) 4
(c) 9
(d) None of these

Ans. (b)

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

Ans. (c)

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

Ans. (b)

Ques. If log10 x = 2log10 (5.87) â€“ 1/2 log10 (0.839). Then the value of â€˜xâ€™ is
(a) 37.6
(b) 42.8
(c) 32.4
(d) 21.6

Ans. (a)

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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

Ans. (d)

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

Ans. (b)

Ques. If x = 27, y = log 34, then xy = ___
(a) 64
(b) 16
(c) 4
(d) 1

Ans. (a)

Ques. If log30 3 = x and log30 5 = y, then log30 8 is
(a) 3(1â€“ x â€“ y)
(b) 3(1 + x â€“ y)
(c) 3(1 + x + y)
(d) 3(x + y)

Ans. (a)

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

Ans. (b)

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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

Ans. (c)

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

Ans. (c)

Ques. If log (10x + 5) â€“ log(x â€“ 4) = 2, then the value of â€˜xâ€™ is
(a) 3.5
(b) 2.5
(c) 5.5
(d) 4.5

Ans. (d)

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

Ans. (a)

Ques. If a = 1 + log102 â€“ log 105, b = 2 log103Â  andÂ  c = log10m â€“ log105, then the value of â€˜mâ€™ if a + b = 2c is
(a) 25
(b) 36
(c) 40
(d) 30

Ans. (d)

Ques. If x = logb a, y = logc b, z = loga c, then xyz is
(a) 0
(b) 1
(c) 3
(d) None

Ans. (b)

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

Ans. (a)

Ques. If 7x+1 â€“ 7xâ€“1 = 48. Then the value of â€˜xâ€™ is
(a) 7
(b) 0
(c) 1
(d) 2

Ans. (c)

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

Ans. (b)

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