16. The value of 25 log₅ 4 is ?

1. 1. 16

   
   
   

   2. 5

   
   
   

   3. 25

   
   
   

   4. None of these

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Exp. = 25 log₅4 = 5² log₅4
   = 5 log₅ 4²

   Correct Option: A

   Exp. = 25 log₅4 = 5² log₅4
   = 5 log₅ 4²
   = 16
   

---

17. If log₁₀ {log₁₀[log₁₀(log₁₀N )]} = 0, then the value of N is ?

1. 1. 10¹⁰

   
   
   

   2. 10¹⁰¹⁰

   
   
   

   3. 10^-10

   
   
   

   4. 10¹⁰²

   
   
   

---

1. View Hint View Answer Discuss in Forum

   If log₁₀{log₁₀[log₁₀(log₁₀N)]} = 0
   ⇒ log₁₀{log₁₀(log₁₀N)} = 1
   ⇒ log₁₀(log₁₀N) = 10

   Correct Option: B

   If log₁₀{log₁₀[log₁₀(log₁₀N)]} = 0
   ⇒ log₁₀{log₁₀(log₁₀N)} = 1
   ⇒ log₁₀(log₁₀N) = 10
   ⇒ log₁₀^N = 10¹⁰
   ∴ N = 10¹⁰¹⁰
   

---

---

18. log_-1/3 81 is equal to ?

1. 1. - 27

   
   
   

   2. - 4

   
   
   

   3. 4

   
   
   

   4. 127

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let log_-1/381 = x
   ⇒ 81 = (-1/3)^x
   ⇒ 3⁴ = (-1/3)^x = 3^-x

   Correct Option: C

   Let log_-1/381 = x
   ⇒ 81 = (-1/3)^x
   ⇒ 3⁴ = (-1/3)^x = 3^-x
   ∴ x = -4
   

---

19. log₁₀x + log₁₀y = z, then x is equal to ?

1. 1. z / y

   
   
   

   2. 10 / z

   
   
   

   3. 10² / x

   
   
   

   4. None of these

   
   
   

---

1. View Hint View Answer Discuss in Forum

   log₁₀xy = z
   ⇒ xy = 10^z
   

   Correct Option: D

   log₁₀xy = z
   ⇒ xy = 10^z
   ⇒ x = 10^z/y
   

---

---

20. log₁₀10 + log₁₀100 + log₁₀1000 + log₁₀10000 + log₁₀100000 is equal to ?

1. 1. 15

   
   
   

   2. log 11111

   
   
   

   3. log₁₀¹¹¹¹

   
   
   

   4. 14 log₁₀ 100

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Given Exp. = log₁₀10 + log₁₀100 + log₁₀1000 + log₁₀10000 + log₁₀100000
   = 1 + 2 + 3 + 4 + 5

   Correct Option: A

   Given Exp. = log₁₀10 + log₁₀100 + log₁₀1000 + log₁₀10000 + log₁₀100000
   = 1 + 2 + 3 + 4 + 5
   = 15
   

---