## DLS 2 years ago Domain of this function

1. DLS

$\LARGE \log_2[\log_3(\log_4x)]$

2. ParthKohli

The domain of $$\log_4 x$$ is _ ^_^?

3. DLS

How do we proceed? $\log_4x>0 ~or \log_3(\log_4x)>0?$

4. DLS

@ParthKohli do methodwise :|

5. ParthKohli

Let $$\log_3 (\log_4(x)) = a$$. You have $$\log _2 (a)$$. The domain of that is...?

6. AravindG

use the domain of log in each case ..making note of what is the base,and values possible for each log function

7. DLS

@ParthKohli idk =)

8. ParthKohli

Remember that in the case of logs, the domain is $$a > 0$$.

9. DLS

oh yeah i know that :O

10. DLS

so?

11. ParthKohli

12. DLS

NO :/

13. ParthKohli

You should also remember that $$\log(x) > 0$$ so it is needless to say that $$a > 0$$.

14. DLS

15. ParthKohli

Of course that is the answer to your question.$\{ x \in \mathbb R : x > 0\}$

16. DLS

arre nahi hai bc :/

17. ParthKohli

lol

18. shubhamsrg

log2(log3(log4x)) for log2 ( ) to be defined, log3(log4x) >0 that'll mean log4x >1 , hence x>4 ^_^

19. ParthKohli

Just kidding.$x > 4$

20. DLS

winner

21. ParthKohli

Arrey yeh Shubham jeet gaye!

22. shubhamsrg

:')

23. DLS

log3(log4x) >0 that'll mean log4x >1 , hence x>4 ??

24. shubhamsrg

yes, sahi kaha :P

25. DLS

kya matlab

26. ParthKohli

Main toh bhool hi gayi thee ki bases bhi hain. lolol

27. shubhamsrg

ye to clear hai ki log3(log4x) > 0 hoga. log 1 = 0, kisi bhi base pe (except 1) hence log4x > 1 hona chaiye h a i n a ?

28. DLS

29. ParthKohli

$\log_a b = \dfrac{\log b}{\log a}$

30. DLS

so much win by writing that

31. DLS
32. ParthKohli

8-)

33. ParthKohli

So much sarcasm! ^_^

34. DLS

no one failed to make me understand till now :3

35. DLS

i mean everyone failed lol

36. shubhamsrg

only one man can save they day he is right here, looking at the question, in silence! is this silence before the storm ? my dear friend, we will know soon, we all know who that person is! comeon @yrelhan4 :')

37. DLS

arre yaar tum log quality answers do :/

38. ParthKohli

:-)

39. shubhamsrg

chala gay :P

40. shubhamsrg

gaya* :|

41. DLS

oh gawd i have to waste another hour on this -_- just one dam question

42. DLS

lol lololol @yrelhan4 jhand

43. ParthKohli

Sorry guys I have IIT JEE at 3 am gotta go

44. DLS

$\LARGE \log_3{(\log_4x)}>0$

45. DLS

what next

46. shubhamsrg

abe yaar, sachin ponting dono out :/

47. ParthKohli

Haan yaar, Dinesh hai :-]

48. DLS

49. shubhamsrg

10 overs 95 runs, banega? :/

50. ParthKohli

Nahi banega!

51. ParthKohli

Gayle hai na banda! 8-)

52. DLS

f u c k y o u g u y s :/ just answer it

53. yrelhan4

Meri besti kregi to mai nhi btaunga aata bhi hoga to. :/

54. yrelhan4

krego*

55. shubhamsrg

sharma jita dega mujhe intuition aa raha hai :)

56. DLS

57. ParthKohli

$\log_3 (\log_4 x) > 0$Dono sides ka exponentiation karo!

58. DLS

kaise karte hai hai !

59. shubhamsrg

main kabhi tumhari bezzati nahi kRERta @yrelhan4 , sach to sach hota hai :/

60. shubhamsrg

kregta*

61. DLS

STOP IT :/

62. shubhamsrg

hmm, log3(log4x)=0 hai find x ?

63. DLS

wahi puch r aha hoon kaise

64. ParthKohli

Yeah, minimum value^

65. ParthKohli

log ko clear karo

66. shubhamsrg

log(base 3) 1 = 0?

67. DLS

log nahi ata :P

68. shubhamsrg

"0" nahi bolna tha mujhe -_-

69. ParthKohli

$1 = \log_4 (x)$^_^

70. yrelhan4

log nhi aata to kya krega. :/

71. DLS

batao to dhang se :/

72. ParthKohli

$x = 0$^_^

73. 50_cent

nice job

74. ParthKohli

But!

75. DLS

$\LARGE 3^{\log_3(\log_4x)}>3^0$

76. DLS

explain how did we get this:\

77. ParthKohli

Dono sides mein 3 ki power ko kar diya hai.$a = b \implies 3^a = 3^b$

78. shubhamsrg

a>b>=0, to x^a > x^b hai na?

79. DLS

3 se kyn kiya?

80. ParthKohli

Because woh $$\log_3$$ ka ulta hai!

81. shubhamsrg

yaar ye log itne gande run rate se khel rahe hain! -_-

82. DLS

3 raise to the power log3?

83. yrelhan4

abbe answer de to diya usne? x>4 galat hai? :O

84. ParthKohli

$2x = 3$$\implies x = \dfrac{3}{2}$2 se divide kyun kiya? Arrey bhai, 2 se multiply karne ka ulta 2 se divide karna honda hai

85. ParthKohli

$3^{\log_3 a} = a$

86. DLS

sahi hai par dafuq :/

87. DLS

haan bus wahi sunna tha :P

88. DLS

someone teach me logs someday,ill pay \$5

89. ParthKohli

Iske liye itna tang kar rakha tha -_-

90. ParthKohli

5 theoretical dollars?! Manzoor hai!

91. DLS

yesh! Paypal

92. yrelhan4

Ok bye.

93. ParthKohli

Bhaiya, ab logs ko aap intuition se dekho

94. yrelhan4

@shubhamsrg Medal?

95. ParthKohli

96. shubhamsrg

pehle bhi bataya hai maangne pe nahi deta :/

97. DLS

lol

98. DLS

99. ParthKohli

Dekho, $$\log_a b$$ gets you a value which you raise to $$a$$ to get $$b$$.

100. DLS

thanks,closed

101. ParthKohli

Bas yahi hote hain logs

102. DLS

:"D

103. ParthKohli

Trigonometry bhi kya hoti hai? Bas 3 ratio hote hain aur kya!

104. DLS

Calculus,dy/dx

105. yrelhan4

Fir se batane ke liye medal @shubhamsrg :P

106. ParthKohli

Haan, aur kya, bas rate of change hi hota hai integral aur differential calculus!

107. DLS

2+2=maths

108. ParthKohli

Aur kya! Maths is too simple! Bas ye pata karo ki $$1 + 1 = 2$$ aur baaki derive kar lo!

109. DLS

110. DLS

63/68 karke dikhado drawing se @yrelhan4 @shubhamsrg @ParthKohli

111. ParthKohli

$1 + 1 + 1 + 1$ko$1 + 1$parts mein divide karo

112. DLS

mai seriously bhool gaya kaise karte hai :/

113. ParthKohli

Asaan hai!|dw:1365096919950:dw|

114. shubhamsrg

1 baar 1 ladki 1 dukandaar ke paas gayi, bolo, "calculator dikhao" dukaandaar bola, "casio?" ? wo boli, " mai badhiya, aap sunao"!! ^_^

115. shubhamsrg

boli*

116. ParthKohli

Thanks for the wonderful... PJ...

117. shubhamsrg

:)

118. DLS

|dw:1365097203822:dw|

119. ParthKohli

|dw:1365097240971:dw|

120. DLS

thanks

121. ParthKohli

Bahut raat ho gayi hai... 2 AM ho gaya hai. Bye

122. shubhamsrg

5 ovr, 60 runs, last ball tak jayega match! :O TV nahi hai mere paas :'(