7. If
a  log 24 12 , b  log36 24 , c  log 48 36 , then
value of (1 + abc) is :
1. If log7 2  m , then log 49 28 , is equal to :
(a) 2(2m + 1)
(c)
(b)
2
2m  1
2m  1
2
ab 1

2. If ln 
   ln a  ln b  , where a , b  R then
 2  2
relation between a and b is :
(a) a = b
b
2
(c) a = 2b
(d) a 
b
3
3. The value of
(81) log5 3  (27)log9 36  (3) log7 9
4
(d) 890
(b) 1
(c) log 2
(d) log 3
5. If A  log 2  log 2 log 4 256    2log
(a) 2
(b) 3
(c) 5
(d) 7
10.
(b) 1
(c) 2
(d) 3
 log (tan(r
3
o
)) is equal to :
(a) 3
(b) 1
(c) 2
(d) 0
1
 log
r 1
2r
a
is equal to :
(a)
n(n  1)
log a 2
2
(b)
(c)
(n  1)n . n2
log2 a
4
(d) none of these

n(n  1)
log2 a
2

11. If log 7 log5 ( x 2  x  5)  0 , then x is equal to :
2
2 , then A is :
(a) 2
(b) 3
(c) 4
(d) –2
12. The value of (0.05)
6. If x  log a (bc) , y  logb (ac ) , z  logc (ab) , then
which one of the following is equal to 1 ?
(a) 81
(c) 20
(a) x  y  z
1
1
1


(b)
1  x 1  y 1 z
(a) 0
n
is :
 16 
 25 
 81 
4. 7 log    5 log    3 log   is equal to :
 15 
 24 
 80 
(a) 0
(d) 0
r 1
1
(c) 216
(c) 2bc
89
9.
(b) a 
(b) 625
(b) 2ac
8. If a x  b , b y  c , c z  a , then value of (xyz) is :
(d) m + 1
(a) 49
(a) 2ab
log
20
( 0.1 .01.001 .....  )
is :
1
81
(d) 10
(b)
13. If log12 27  a , then log6 16 is :
(c) x y z
(d) (1  x)2  (1  y )2  (1  z ) 2
[ 58 ]
3 a 
(a) 2 

 3 a 
 3 a 
(b) 3 

3a 
 3 a 
(c) 4 

 3 a 
4a
(d) 2 

4a
Page 1
Logarithm
14. If n  2010! , then
1
1
1

 ....... 
is
log 2 n log 3n
log 2010 n
equal to :
x2 2x

1
, then set of 'x' contains :
4
(a) –1
(b) 0
(a) ( , 0)
(b) ( , 1)
(c) 1
(d) 2
(c) (1 , )
(d) none of these
15. The number of solution(s) of log 2 ( x  5)  6  x
is/are :
(a) 2
(b) 0
(c) 3
(d) 1
 5 1 
, 1
(a) 
 2


(b)  0 ,

1
(c)  0 , 
2

 5 1
,
(d) 
 2
log
1
2
5  1

4 
values of x which are integral multiples of
(b) 12
(c) 3
(d) 10
(a) [0 , 4]
(b) (0 , 4] – {1}
(c) (0 , 4)
(d) none of these
23. The value of
5  1

2 
(sin x )  0 , x  [0 , 4 ] , then number of
(a) 4
 5x  x2 
  0 , then exhaustive set of values
 4 
22. If log x 
of x is :
16. If logcos x sin x  2 , then the values of sin x lies in
the interval :
17.
1
21. If  
 2

, is :
4
log 2 24 log 2 192

is :
log96 2
log12 2
(a) 3
(b) 0
(c) 2
(d) 1
7
24. If log3 2 , log3 (2 x  5) and log3  2 x   are in A.P. ,
2

then x is equal to :
(a) 2
(b) 3
(c) 4
(d) 8
25. If log x 2  log 2 x  3log 3  log 6 , then x is :
18. Set of real values of x satisfying the inequation
(a) 10
(b) 9
(c) 1
(d) 2
2
log0.5 ( x  6 x  12)  2 is :
(a) ( , 2]
(b)  2 , 4
(c) [4 , )
(d) none of these
3
19. Set of real x for which 2
,
log
2
( x 1)
26. If ( x) 4
 ( x  5) is :
(a) ( ,  1)  (4 , )
(b) (4 , )
(c) (–1 , 4)
(d) [1 , 4)  (4 , )
5
4
 3 , then x has :
(a) one positive integral value.
(b) one irrational value.
(c) two positive rational values.
(d) no real value.
x2
20. If log0.2 
  1 , then x belongs to :
 x 

 log3 x 2 log3 x 
27. If x  9 satisfy the equation
5
(a)   ,    (0 ,  )
2
 8ax 
ln( x 2  15a 2 )  ln(a  2)  ln 
 , then
a2
5

(b)  ,  
2

(a) value of 'a' is 3

(b) value of 'a' is
(c) ( ,  2)  (0 , )
9
5
(c) x = 15 is other solution
(d) none of these
(d) x = 12 is other solution
[ 59 ]
Page 2
28. Let p 
ln 3
, then the correct statements are :
ln 20
(a) p is a rational number
31. Let x  (1 , ) and y  (1 , 16) , where xy = 16. If x
(b) p is an irrational number
1 1
(c) p lies in  , 
3 2
and y satisfy the relation log y x  log x y 
value of ( x  y ) is equal to ..........
1 1
(d) p lies in  , 
 4 3
29. Let set 'S' contain the values of x for which the
equation
x 1
 log10 x 2  log10 x 2
8
, then
3

32. If a  R  {1} ,  
 | x  1|3 is satisfied ,

then :
(a) total number of elements in 'S' are 4
 x
log10  
(3)  10 
6 log a x.log10 a.log a 5
(a)
and
5
 (9)log100 x  log 4 2 , where     0 ,
x
is equal to ..........
4
then value of
(b) set 'S' contains only one fractional number
(c) set 'S' contains only one irrational number
4
(d) total number of elements in 'S' are 2
33. If M 
r 

 log  sin  5   , then value of (2)
2
M 4
is
r 1
30. If set 'S' contains all the real values of x for which
equal to ..........
log( 2 x  3) x 2  1 is true , then set 'S' contain :
(a)  log 2 5 , log 2 7 
34. If
(b) log3 4 , log38
 (a )
 3 
(c)   , 1
 2 
(d) (1 , 0)
ln a
lnb
ln c


,
( y  z ) ( z  x) ( x  y )
y 2  yz  z 2
.(b) z
2
 zx  x 2
.(c ) x
2
then
 xy  y 2

value of
is equal to
..........
35. Total number of integral solution(s) of the equation
x  log10 (2 x  1)  xlog10 5  log10 6 is/are ..........
[ 60 ]
Page 3
Logarithm
1. (b)
2. (a)
3. (d)
4. (c)
5. (c)
6. (b)
7. (c)
8. (b)
9. (d)
10. (a)
11. (c)
12. (a)
13. (c)
14. (c)
15. (d)
16. (b)
17. (a)
18. (b)
19. (b)
20. (a)
21. (d)
22. (b)
23. (a)
24. (b)
25. (b)
26. (a , b , c)
27. (a , c)
28. (b , c)
29. (a , b)
30. (a , b , d)
31. ( 6 )
32. ( 5 )
33. ( 5 )
34. ( 1 )
35. ( 1 )
[ 61 ]
Page 4