11. 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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12. log₉ 27 - log₂₇ 9 is equal to ?

1. 1. 6 / 5

   
   
   

   2. 5 / 6

   
   
   

   3. 3

   
   
   

   4. 3²

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given Exp. = log₉27 - log₂₇9
   = log27 / log9 - log9 / log27
   

   Correct Option: B

   Given Exp. = log₉27 - log₂₇9
   = log27 / log9 - log9 / log27
   = 3log3 / 2log3 - 2log3 / 3log3
   = 3/2 - 2/3 = 5/6
   

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13. If log 125 / log 5 = x, then x is equal to ?

1. 1. 2

   
   
   

   2. 3

   
   
   

   3. 4

   
   
   

   4. 1 / 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   If log 125 / log 5 = x
   then x = 3log5 / log5= 3
   

   Correct Option: B

   If log 125 / log 5 = x
   then x = 3log5 / log5= 3
   

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14. (log₅ 3 ) x (log₃ 625) is equal to ?

1. 1. 1

   
   
   

   2. 2

   
   
   

   3. 3

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   (log₅3) x log₃ 5⁴ = [log3 / log5] x 4 x [log5 / log3]
   = 4
   

   Correct Option: D

   (log₅3) x log₃ 5⁴ = [log3 / log5] x 4 x [log5 / log3]
   = 4
   

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15. If log₁₀ (10x) = 2.7532, then log₁₀ (10000x) is ?

1. 1. 4.7532

   
   
   

   2. 5.7532

   
   
   

   3. 3 x 2.7532

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   log₁₀(10³.10x) = log₁₀ 10³ + log₁₀(10x)
   

   Correct Option: B

   log₁₀(10³.10x) = log₁₀ 10³ + log₁₀(10x)
   = 3 + 2.7532
   = 5.7532
   

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