Logarithms

1

If log log2 (5 + log3 a) = 3 and log5 (4a + 12 + log2 b) = 3, then a + b is equal to

  1. 67
  2. 40
  3. 32
  4. 59
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2

Log (402 - 202) is equal to

  1. log 3
  2. log 60 + log 20
  3. log 40 – log 20
  4. log 20
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3

If log25 5 = a and log25 15 = b, then the value of log25 27 is

  1. 3(b+a)
  2. 3(1-b-a)
  3. 3(a+b-1)
  4. 3(1-b+a)
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4

What is the solution of the equation
x log10 (10/3) + log10 3 = log10 (2 + 3x) + x?

  1. 10
  2. 3
  3. 1
  4. 0
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5

If x is a real number such that log3 5 = log5 (2 + x), then which of the following is true?

  1. 0 < x < 3
  2. 23 < x < 30
  3. x > 30
  4. 3 < x < 23
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6

If log3 2, log3 (2x - 5), log3 (2x - 7/2) are in arithmetic progression, then the value of x is equal to

  1. 2
  2. 3
  3. 4
  4. 5
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