DPP: Logarithms | AP Precalculus - Grade 9 PDF Download

 Page 1


Topic : Logarithm
Type of Questions M.M., Min.
Single choice Objective (no negative marking) Q.1,2,3 (3 marks, 3 min.) [9, 9]
Multiple choice objective (no negative marking) Q.4,5 (5 marks, 4 min.) [10, 8]
Subjective Questions (no negative marking) Q.6,7 (4 marks, 5 min.) [8, 10]
1. If log
7
 log
2
 log
? 
x vanishes, then x equals:
(A) ?
2
(B) 4 (C) 49 (D) none
2. If  log
3
x = a and log
7
x = b, then which of the following is equal to log
21
x ?
(A) ab (B) 
1 1
b a
ab
? ?
?
(C) 
b a
1
?
(D) 
1 1
b a
1
? ?
?
3. Let  N = 
409
3 81
3 log
3
9 log
1
6 5
?
 . 
? ?
?
?
?
?
?
?
?
?
?
6 log
7 log
2
25
25 125 7
, then value of log
2
N is equal to :
(A) 0 (B) 1 (C) –1 (D) none
4. If  ?n
 
(x
 
+
 
z) + ln (x ? 2y
 
+
 
z) = 2 ln
 
(x ? z),  then :
(A)  y = 
2xz
x z ?
(B)  y
2
 = xz (C)  2y = x + z (D) 
x
z
 = 
x y
y z
?
?
5. Which of the following when simplified reduces to unity ?
(A) log
1.5
 log
4
 
3
log
81 (B) log
2
6
 + log
2
3
2
(C) – 
6
1
 
2
3
log 
?
?
?
?
?
?
27
64
(D) log
3.5 
(1 + 2 + 3
?
6)
6. If 
8
log b = 3
3
1
, then b is equal to ......
7. Which is greater
(i)  
3
1
log
80
1
   or   
2
1
log
?
?
?
?
?
?
?
?
? 2 15
1
(ii) log
3 
5  or  25 log
17
(iii)  
5
1
log
7
1
  or    
7
1
log 
5
1
Page 2


Topic : Logarithm
Type of Questions M.M., Min.
Single choice Objective (no negative marking) Q.1,2,3 (3 marks, 3 min.) [9, 9]
Multiple choice objective (no negative marking) Q.4,5 (5 marks, 4 min.) [10, 8]
Subjective Questions (no negative marking) Q.6,7 (4 marks, 5 min.) [8, 10]
1. If log
7
 log
2
 log
? 
x vanishes, then x equals:
(A) ?
2
(B) 4 (C) 49 (D) none
2. If  log
3
x = a and log
7
x = b, then which of the following is equal to log
21
x ?
(A) ab (B) 
1 1
b a
ab
? ?
?
(C) 
b a
1
?
(D) 
1 1
b a
1
? ?
?
3. Let  N = 
409
3 81
3 log
3
9 log
1
6 5
?
 . 
? ?
?
?
?
?
?
?
?
?
?
6 log
7 log
2
25
25 125 7
, then value of log
2
N is equal to :
(A) 0 (B) 1 (C) –1 (D) none
4. If  ?n
 
(x
 
+
 
z) + ln (x ? 2y
 
+
 
z) = 2 ln
 
(x ? z),  then :
(A)  y = 
2xz
x z ?
(B)  y
2
 = xz (C)  2y = x + z (D) 
x
z
 = 
x y
y z
?
?
5. Which of the following when simplified reduces to unity ?
(A) log
1.5
 log
4
 
3
log
81 (B) log
2
6
 + log
2
3
2
(C) – 
6
1
 
2
3
log 
?
?
?
?
?
?
27
64
(D) log
3.5 
(1 + 2 + 3
?
6)
6. If 
8
log b = 3
3
1
, then b is equal to ......
7. Which is greater
(i)  
3
1
log
80
1
   or   
2
1
log
?
?
?
?
?
?
?
?
? 2 15
1
(ii) log
3 
5  or  25 log
17
(iii)  
5
1
log
7
1
  or    
7
1
log 
5
1
1. (A) 2. (D) 3. (A) 4. (A)(D)
5. (A)(B)(C)(D) 6. b = 32
7. (i)
2
1
log
?
?
?
?
?
?
?
?
15 ? 2
1
(ii) log
3
5 (iii)
5
1
log
7
1