31. The value of log₆ log₅ 15625 is ?

1. 1. 1

   
   
   

   2. 2

   
   
   

   3. 3

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   log₆ log₅15625 = log₆ log₅(5)⁶
   

   Correct Option: A

   log₆ log₅15625 = log₆ log₅(5)⁶
   = log₆6(log₅5) = 1

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32. If log₁₀₀₀₀x = -1/4, then x is ?

1. 1. 1 / 100

   
   
   

   2. 1 / 10

   
   
   

   3. 1 / 20

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   ∵ log₁₀⁴x = -1/4
   ⇒ x = (10⁴)^-1/4
   = 1/10
   

   Correct Option: B

   ∵ log₁₀⁴x = -1/4
   ⇒ x = (10⁴)^-1/4
   = 1/10
   

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33. log_x (16/25) = -1/2, then x is ?

1. 1. 625 / 256

   
   
   

   2. 256 / 625

   
   
   

   3. 526 / 265

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   ∵ log_x(16/25) = -1/2
   ⇒ 16/25 = (x)^-1/2 = 1/x^1/2
   

   Correct Option: A

   ∵ log_x(16/25) = -1/2
   ⇒ 16/25 = (x)^-1/2 = 1/x^1/2
   ∴ x = 625/256
   

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34. The value of log₂ (1/64) is ?

1. 1. 6

   
   
   

   2. - 6

   
   
   

   3. 7

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   log₂(1/64) = log₂1 - log₂ 2⁶
   
   

   Correct Option: B

   log₂(1/64) = log₂1 - log₂ 2⁶
   = 0 - 6 = -6
   

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35. If log_a 3 = 1/3, then value of a is ?

1. 1. 27

   
   
   

   2. 81

   
   
   

   3. 72

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   ∵ log_a3 = 1/3
   ⇒ 3 = (a)^1/3

   Correct Option: A

   ∵ log_a3 = 1/3
   ⇒ 3 = (a)^1/3
   ∴ a = 27
   

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