31. If log₁₀ 2 =0.301, then the value of log₁₀(50) is ?

1. 1. 0.699

   
   
   

   2. 1.301

   
   
   

   3. 1.699

   
   
   

   4. 2.301

   
   
   

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1. View Hint View Answer Discuss in Forum

   log₁₀50 = log₁₀[(50 x 2) / 2]
   = log 100 - log 2
   = log₁₀10² - log 2

   Correct Option: C

   log₁₀50 = log₁₀[(50 x 2) / 2]
   = log 100 - log 2
   = log₁₀10² - log 2
   = 2 - 0.301
   = 1.699
   

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32. Find the value of log (a² / bc) + log (b² / ac) + log (c² / ab) ?

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. abc

   
   
   

   4. ab²c²

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given Exp. = log (a² / bc) + log (b² / ac) + log (c² / ab)
   = log [(a² x b² x c²) / (a^{2 x} b² x c²)]
   

   Correct Option: A

   Given Exp. = log (a² / bc) + log (b² / ac) + log (c² / ab)
   = log [(a² x b² x c²) / (a^{2 x} b² x c²)]
   =log 1
   =0
   

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33. Find the value of log 8 + log 1/8 ?

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 2

   
   
   

   4. log (64)

   
   
   

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1. View Hint View Answer Discuss in Forum

   log 8 + log (1/8) = log (8 x1/8) = log 1 = 0
   

   Correct Option: A

   Given expression = log 8 + log (1/8)
   = log 8 x (1/8)
   = log 1
   = 0
   

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34. If log 2 = 0.3010, then the number of digits in 2⁶⁴ is ?

1. 1. 18

   
   
   

   2. 19

   
   
   

   3. 20

   
   
   

   4. 21

   
   
   

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1. View Hint View Answer Discuss in Forum

   Required answer = [64 log₁₀ 2] + 1

   Correct Option: C

   Required answer = [64 log₁₀ 2] + 1
   = [ 64 x 0.3010 ] + 1
   = 19.264 + 1
   = 19 + 1
   = 20
   

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35. Find the value of log x + log (1/x) ?

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. - 1

   
   
   

   4. 1/2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given expression = log x + log1/x
   = log x + log 1 - log x
   

   Correct Option: A

   Given expression = log x + log1/x
   = log x + log 1 - log x
   = log 1
   = 0
   

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