36. If log₁₀ x = 7, then value of x is ?

1. 1. 10¹⁰

   
   
   

   2. 10⁷

   
   
   

   3. 7¹⁰

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   log₁₀x = 7
   ∴ x = 10⁷
   

   Correct Option: B

   log₁₀x = 7
   ∴ x = 10⁷
   

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37. If p^x = q, then ?

1. 1. log_p x = q

   
   
   

   2. log_x q = P

   
   
   

   3. log_p q = x

   
   
   

   4. log_q P = x

   
   
   

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1. View Hint View Answer Discuss in Forum

   ∵ p^x = q
   ⇒ log_pp^x = log_pq
   

   Correct Option: C

   ∵ p^x = q
   ⇒ log_pp^x = log_pq
   ⇒ xlog_pp = log_pq
   ∴ x = log_pq (∵log_pp = 1)
   

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38. Given that log₁₀ 2 = 0.3010 the value of log₁₀ 5 is ?

1. 1. 0.3241

   
   
   

   2. 0.6911

   
   
   

   3. 0.6990

   
   
   

   4. 0.7525

   
   
   

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1. View Hint View Answer Discuss in Forum

   log₁₀5 = log₁₀(10/2)
   = log₁₀10 - log₁₀2
   = 1-0.3010
   
   

   Correct Option: C

   log₁₀5 = log₁₀(10/2)
   = log₁₀10 - log₁₀2
   = 1-0.3010
   = 0.6990
   

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39. 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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40. 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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