TEST YOUR CONCEPTS

Very Short Answer Type Questions

1. log,A" = 18. If 2logx + 2logy =k and xy=1, then k=

19. If log 198.9 = 2.2987, then the characteristic of
2. Expandlogs
log 198.9= andmantissaof log 198.9 =

log,a, 20. When 0 < a<1 and m <n, then which is greater,
3. Can we write logx, as
b log,b logm (or) log.i?

4. Express 0.001 = (0.1) in the logarithmic form. 21. Given logox= y. If the characteristic of y is 10,
then the number of digits to the left the decimal
5. (5)2log,2= point inx is
6. logs2 + log;20 - log,8 = 22. Find thevalue of logl6.
The value of 3+logıo(10)2 1s 23. log,x x log_y X logz
log, 5
24. If the characteristics of the logarithm of two
8. log,ab = (log,a) x (og,b). State True or False.
numbers abcd-abef and a-bcdabefare x and y respec-
9. I og:o2 = 0.3010, then log,o 2000 = tively,then x- y =
10. Evaluate 3 - log1o100. 25. I og2=0.3010, log3 =0.477 1 and log7 =0.8451,
11. Given 3 = log,x + 4log,8. Then the value of then nd the values of log 210.
*= 26. Given, antilog(2.375) = x. Characteristic of logx is
12. If log:02=0.3010,then logı5=
13. If x = log,3 andy= log;8, then log;24 in terms of 27. If log(21.73) = 1.3371, then nd the values of
x, y is equal to. log(2.173).
14. If logi625 = k log5, then k =
28. If antilog (0.2156) = 1.643, then nd the values of
15. If5log3 + logx = 5log6, then x= antilog (1.2156).

29. Without using the logarithm tables nd the value

16. I ogx = loga) then k= of 3log,27.
loga
17. If a > 1 and m > n, then which is greater, log," 30. Find thevalueoflogo.
(or) log?

Short AnswerTypeQuestions
31. Prove that log5040 = 4log2 + 2log3 + log5 | 36. Prove that log, [log, {log, (625)}] = 1.
+ log7. 37. If log02 =0.3010, then nd the number of digits
32. Find the value of log,- (0.0625). in (16)10
38. I og2 = 0.3010, 1log3 = 0.4771 and log7 = 0.8451,
33. Express the following as a single logarithm. then nd the value of log75.
8
log*logy+logz. 39. Ifx* + y= 83**y, thenprovethatl
34. If +ỷ= 25xy, then prove that 2log(x + y) = = logx + logy.
3log3 + logx + logy. 40. Prove that

35. If t =2, then prove that log,(z + *) + 35 114

2log197+2log tlog48 +2log
log,(z- x) = 2.
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 41. Solve for x:
43. Using thetables nd the value of (32).
logx + log5=2 +log64
44. Using the tables nd the value of Vo.12.
42. Ifx -yo=, thenprovethat
45. Given log3 = 0.4771, then the number of digits in
log,(- y)+log,(2+ -x) + logtt 31000 is
*y) =6.

Essay Type Questions

46. If log,2x -1 + logz-1* +1 =2, ndx. 49. If log,x- log,a = 9(logs) and x = 9y, nd y.
47. If a=b/s =5 =an =el9, ndlog,abcde.
50. ?
48. Arrange the following in ascending order.

A=log,6561 B=logg625
C=logg243 D=log5256

CONCEPT APPLICATION
Level 1

1. log,4 X logxy =- 5. log_ xy =?

(a) logay (b) log,a (a) 2(logx + logy - logz)

(c) log,a (d) log (b) logx + logy - logz

logx*+logy
2. If logx = 123.242, then the characteristic of logx (c
is log z

(a) 0.242 (b) 122 logx+logy

(d)
log z
(c) 123 (d) 124
6. Ifx-= 3xy(*-y),thenlog(*- )°=
3. Pick up the false statement.
(a) 0 (b) 1

(A) Logarithms are de ned only for positive real (c) Unde ned (d) None of these
numbers.
7. log(a + b)- log(a+b) -log(a - ab+ b) =
(B) log,Nis always unique.
(a) - 3
(C) The log form of 2 =8 is 3 = logg2. (b) 0

(D)log1 =0 (c) log 1

(a) B (b) C (a) Both (b) and (c)

(c) D (d) A 8. Which is greatest among the following:

(a) log,20 (b) log,35

4. log 169)- 2log 13 + 2log3 =?
()logs70 (d logs68

(a) 1 (b) 0 9. log(a+ b) + logla – b) - log(a - ) =

(a) 0 (b) 1

(c)log 3 (c) (a- b) (d) + 2

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 10. Ifx+ y= 4xyl* + y).Thenlog(r +y)'= (a) 11 (b) 121

(a) logx + logy + log(x +y) - log? (c) 0 (d) 1

(b)log(a) - logy + log(x + ) + log7 log,729 +log,216

19.
(c) logx + logy + log(x - ) + log7 4+log,16-2log,64
(d) logx + logy + log(x t) + log7 (a) 9 (b) 4

11. Ir g *_log49 then the relation between x and y. (0

logy log7

(a) x=y 20. If logn yM = klogxy, then the value of kis

(b) x= y
(a) (b) mn
(c)y=
(c) (d) :
(d) x=
12. log(o) – log(2x -3) = 1, then x =? 21. I og,r=2, then log,logy) =
(a) -2 (b) 4
(a) (6)
() 4
() 9
19
() 30 20
22. Ifp = log216 and q = log,25 then p =

13. If 2log(* + 4) = log 16, then x=? (a) 3 (b) 25

(a) 0, -8 (b) -8 (c) 15 (d) Cannot be determined

23. 2(l6-log,1024) =
(c) -2 (d) 0
(a)116 (b) 32
14. The value of x when log, 343 = 3, is
(d) 64 (d) 8
(a) 7 (b) 8
24. 23log 2 +32log, 2 =
(c) 3 (d) 27
(a) 8 (b) 4
15. logı63- log,y4 log, 17 = .
(c) 9 (d) 2

); 25. loga+b(ad+ b')- log+t(a - ab+ b²) =

(a) loga+t{a- b) (b) 2
(c) a+ b (d) 1

26. 4log25 =
16. log, [logs {log2 (logs81)}] =
(a) 1
(a) 25 (b) 5

(c) 16 (d) 4
(b) 0
1 1
(c) log3 27. + ?
logxy * logxy Y
(d) Unde ned
(a) 1 (b) 2
17. logı13 · log,1331 =
(c) 0 (d)
(a) 3 (b) 11
logxy* X logxyY
() 121 (d) 9
28. Ify = log,-s(a- 6x +9), then nd y.
V14641 (a) 4 (b) 8
18. logı21|
121
(c) 2 (d) 32
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 Level 2|

29. If log02 = 0.3010, then the number of digits in 38. If loga " =3 then alogh-loga =
1612 is
(a) 6 (b) 9
(a) 14 (b) 15 (c) 3 (d) Cannot be determined

(c) 13 (d) 16 39. If log {x – 5) + logs(* + 2) = log,8, then *

30. Ifloge,p?=1chen log:- (a) -3 (b) 6

(a) 16 (b) 2 (c) 6, -3 (d) 3, -6

(c) 32 (d) 1 40. I ogx + ) = logx + logy, then x =

31. log,log,log,125 = )
(a) 4 (b) 8
(c) 1 (d)
(c) -1 (d) 1

32. If logx Y O8a) then thevalueof p is 41. If 2l0g5.slog?=glogr,thenlog, V=

p

(a) log,* (b) loga (b)

(c) log,* (d) logaY

(c) (d) 3

33.log 42. If3og *+ogs= 54, nd logx.

(a) 3 (b) 2
(a) loga23 - log z25 + logy
(c) 4 (d) Cannot be determined
(6) loga2 + logy - log z2 43. If logox - log10y = 1 and x + y = 11, then x
()log 3- logy+log25 =

(d) None of these (a) 10 (b) 1

(c) 11 (d) 2
34. If logl4 - Slogs2(*+ 3)] = 0, ndx.
44. If log3 X log,7 x log,8 = x, then nd the value
(a) 32 (b) 8

(c) 3 (d) 5
of

(a) 3 (b) 7
35. Ifx= log, log,log,256,then2log,2 =
(c) 8 (d) 1
(a) 4 (b) 8
45. Thevalueof log,-la-)- log,-t(a +ab+b2)
(c) 2 (d) 1
is (a> b)
36. Iflog 13_) = 2log, 13– log, 5 – x then
(a) 0 (b) 1

(3) 3 (c) Unde ned

(a) a=23/2 (b) x= 23/2 46. Iflog;2 = x,thenthevalueof 10 is

log,24
(c) a= 22/3 (d) = 22/3
1+x 2+3x
37. If log81 - log3 = loga,then 4,8 =
(2) 16
a)- (b)
1-3x
(1) 4 2-3x 3x+1
(C (d)
(3) 2 (4) 8 2+3x 3x+2
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 Level 2

29. If log02 = 0.3010, then the number of digits in 38. Ifaoga" =3 then2logb-oga
1612 is
(a) 6 (b) 9
(a) 14 (b) 15 (c) 3 (d) Cannot be determined

(c) 13 (a) 16 39. If logs(x - 5) + logs(* + 2) = logg8, then x

30. If logsap' = 1f,then log: (a) -3 (b) 6

) 16 (b) 2 (c) 6, -3 (d) 3, -6

) 32 (d) 40. If log(xt) =logx+ logy,thenx=,

31. log, log, log,125 = (a)

(a) 4 (b) 8

())-1 (d) 1
(c)1 (0)
32. If log,xy= , thenthevalueof p is 41. If2log5.
glog?=glog,thenlogs =

(a) logy* (b) log,a (0)

() logg* (a) logaY 1

(a) 3

33.o - 42. If 3log*+ og3 =54, ndlogx.

(a) 3 (b) 2
(a) log23 - logz2/5 + logy (c) 4 (d) Cannot be determined
(b) log2 + logy -logz5/2 43. If log0% - logoY = 1 and x + y= 11, then x
(c) log 23 - logy + logz25
(d) None of these (a) 10 (b) 1

(c) 11 (a) 2
34. Iflogl[4 - 5logs2*+ 3)] = 0, nd x.
44. If log493 X logg7 x log,8 = *, then nd the value
(a) 32 (b) 8
4x
(c) 3 (d) 5 of 3
35. Ifx = log, log,1log,256,then 2log,2= () 3 (b) 7
(c) 8 (d) 1
(a) 4 (b) 8
45. Thevalue of log,la-)- log,- (a + ab + b²)
(c) 2 (d) 1
1S
- (a>b)
(a) 0 (b) 1
36. I ogaA-2log, 13- log, 5 - xthen
(3) 3 (c) Unde ned

(a) a' = 212 (b) x= 23/2 46. If log: 2 =x, then the value of log,72 is
logı,24
(c) a=22/3 (d) = 22/3
37. I og81 log3 = loga, then 4g"= (a)
1+x
(b) 3r 1-3x
(1) 4 (2) 16 2- 3xx+1
(©) (4)
(3) 2 (4) 8 2+3x 3x+2
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 (a) oo (b) 0
47.
(c) 1 (d) Cannot be determined

51. Ifx +- 3xy = 0andx > y,then nd thevalue

(a)-2 (b) –1
oflogsy- ).
() 0 (d) 2

48. If x = 1, (*> ), then nd the value of (b) 4

logr-p (r + ».
(a) -2 (b) 2
() (d) 2
() –1 (d) 1

49. If 3g: + 5log«= 8, then nd thevalueof x. 52. I og3 =0.4771, then nd the number of digits in
(a) 3 (b) 5 3100

() 4 (d) 8 (a) 47 (b) 48

50. log,1 · log:2 log,3 log;4 log,5 . logao0199 (c) 49 (d) 50

Level 3

53. I ogsx– logsy=logs4 + log;2 and x - y=7, then 1

58. The value of
x= 1+ logab C 1+logac b 1+ logbc a

(a) 1 (b) 8 equals

(a) 2 (b) 0
() 7 (d) 6
(c) 1 (d) log abc
54. If log: -1+a-14x+49 =4, ther X=
1 1

(a) 24 (b) -10 59. If+y=,then

log(z+x)) log(z-)
(c) 24, -10 (d) 10
(a) 4 (b)3
55. If lo8P log4 = og=k andpạr =100,then k (c) 2 (d)
2
1

4 8
60. If log2 = 0.301, then nd the number of digits in
21024
1
(a) 14 (6)
(a) 307 ) 308

(c) 309 (d) 310

(d) 2
61. Ifx-y=1, (x> ), then ndthevalueof log- y)
56. If log2 = 0.3010, and log3 = 0.4771 then log 150 (x+ ).
(a) 2 (b) 2

(a) 2.1761 (b) 2.8751 (c) -1 (d)

(c) 2.5762 (d) 2.6126 62. Ifx² +y²-3xy = 0 and x > y, then nd the value
57. If log02 = 0.3010 and log03 = 0.4771, then the oflogslx- ).
value of log10 (a) (b)4

(a) 0.4592. (b) 0.5492.

(C) (d)2
(c) 0.4529, (d) 0.5429. 2
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 2.14 Chapter2

63. If 2log:9+25l0g.> =gog, then x = 1

66. Ifx=log,27 and y = log,27, then -+*=

(a) 9 (b) 8
1
(c) 3 (d) 2
(a (b)
3 9
64. I og,= mand logx = n, then loga)
(c) 3 (d) 1

M mn 67. If logx + 2log6* + 3log16* = 9, then x

(a) (b)
m-n
(a) 6 (b) 36
(c) (d)
m-n (c) 216 (d) None of these

log, 6 -=
65.
log,2+1
(a) log,6 (b) log5

() logıo6 (d) logı030

fl
TEST YOUR CONCEPTS
Very Short Answer TypeQuestions
1. nlogA 16. -1
2. loggx + 2log3Y 3log,z 17. logam
3. No 18. (

4. logo.1(0.001) =3 19. 2; 0.2987

5. 4 20. logan
6. 1 21. 11
8
7. 5
22. 3
8. False 23. 1

9. 3.3010 24. 3
10. 1
25. 2.3222
11. 1512 26. 2
12. 0.6990 27. 0.3371
13. x + y 28. 16.43
14. 1/2 29. 27
15. 32 30. 2

Short Answer Type Questions

32. 4 38. 1.8751

33. log 41. x= 1280

43. 13.45
36. 1
44. 0.04158
37. 13
45. 478

Essay Type Questions

46. 2 49. 3
ah(n+ 1)
47. 25 50. log nn+1)
48. ABCD b 2
2.16 Chapter 2

CONCEPT APPLICATION

Level 1
1. (b) 2. () 3. (b) 4. (b) 5. (d) 6. (c) 7. (d) 8. (a) 9. () 10. (d)
11. (d) 12. (1) 13. (d) 14. (4) 15. (b) 16. () 17. (a) 18. (c) 19. (c) 20. (a)

21. (c) 22. (b) 23. (c) 24. (b) 25. (4) 26. (6) 27. (d) 28. (c)

Level 2

29. (b) 30. (d) 31. (c) 32. (c) 33. (4) 34. (d) 35. (c) 36. (a) 37. (d) 38. (a)

39. (6) 40. (b) 41. (a) 42. (a) 43. (a) 44. (4) 45. (b) 46. (b) 47. (a) 48. (c)

49. (b) 50. (b) 51. () 52. (b)

Level3

53. (b) 54. (c) 55. () 56. (a) 57. (a) 58. (a) 59. () 60. (c) 61. (c) 62. (c)
63. (b) 64. () 65. (c) 66. (d) 67. (c)