## King 4 years ago Its a log problem which has sqrt so i shall post in reply...

1. King

$\log_{4} \sqrt[4]{32\sqrt[3]{16\sqrt{64.8^{-3\div4}}}}$

2. Ishaan94

2^5 = 32 2^4 = 16 Is it 64 x 8? or 64.8

3. King

its 64 x 8^-3/4

4. King

5. Ishaan94

2^3 = 8 2^6 = 64 Now try it

6. Ishaan94

I don't like this problem

7. King

wait even i dont like it

8. Ishaan94

It's not hard but it's unnecessary

9. King

its necessary for me

10. sheg

1.019

11. King

i am not getting it can u xplain

12. Ishaan94

oh cool sheg

13. King

14. sheg

how come plz explain m right

15. King

idk answer given as 121/186 or 0.6505376

16. sheg

ok wait i made one mistake now i got it

17. Ishaan94

I am getting .7 after simplifying and calculating it in the calculator

18. King

do not use claculator

19. King

and explain

20. King

u should get it as 121/186

21. Ishaan94

King It's a big waste of time, it's not worth it

22. King

pls ishaan its necessary fr me

23. King

sheg wat abt u?

24. sheg

trying to solve it manually

25. Ishaan94

Hmm I am not posting the complete solution, Just a little simplification $\frac{1}{4} \left(\log_4 32 + \frac{1}{3}\left(\log_416 + \frac{1}{2}\left(\log_4 64 + \log_4 8^{\frac{-3}{4}} \right)\right)\right)$

26. sheg

is that 64 times 8?????????????

27. Ishaan94

Now you should do it on your own, I really don't like calculating Numbers

28. King

how did u get 1/4

29. King

yeah sheg

30. sheg

oh got i was taking 64.8

31. Ishaan94

Yeah Sheg

32. Ishaan94

Read the FIITJEE Module for Logs it's the basic property of Log

33. sheg

nahi yar mein usko decimal mein le raha tha na bracket use kiya hai isne na kuch

34. King

wait im reading and i gave u this sum from FIITJEE compendium

35. King

sry sheg are u now getting right answer?

36. Ishaan94

Hmm mujhe bhi same confusion hua tha

37. sheg

i m getting this thing $\log_{4} 2^{\frac{167}{96}}$

38. King

what is that 2^?

39. sheg

167/96

40. King

thats 0.8 sumthing...

41. King

ishaan i calculated ure equation i got 29/32

42. Ishaan94

you must have calculated it wrong

43. King

wait i am checking for mistake

44. Ishaan94

I am getting 127/192 I hate this problem, I hate calculating numbers

45. Ishaan94

.661458333 <<Calculator

46. King

u need to subtract 6 frm numerator and denom. to get rite answer so thatt means u are very close

47. KatrinaKaif

Took me forever to get to the bottom of this >.>

48. King

so post solution katrina

49. King

ishaan what is simplified version of log8^-3/4 base4

50. Tomas.A

$\log_4\sqrt[4]{32\sqrt[3]{16\sqrt{64\cdot8^{-\frac{3}{4}}}}}=$ $\log_4\sqrt[4]{2^5\sqrt[3]{2^4\sqrt{2^6\cdot2^{-\frac{9}{4}}}}}=$ $\log_4\sqrt[4]{2^5\sqrt[3]{2^4\sqrt{2^{\frac{15}{4}}}}}=$ $\log_4\sqrt[4]{2^5\sqrt[3]{2^4\cdot{2^{\frac{15}{8}}}}}=$ $\log_4\sqrt[4]{2^5\sqrt[3]{{2^{\frac{47}{8}}}}}=$ $\log_4\sqrt[4]{2^5\cdot{{2^{\frac{47}{24}}}}}=$ $\log_4\sqrt[4]{{{2^{\frac{167}{24}}}}}=$ $\log_{2^2}2^{\frac{167}{96}}=$ $\log_{2}2^{\frac{167}{192}}=$ $\frac{167}{192}$

51. Ishaan94

Yeah I did it again I am getting the same

52. King

can u explain the 4th step

53. King

how did u take out 2^15/4?

54. Tomas.A

$2^4\cdot2^{\frac{15}{8}}=2^{4+\frac{15}{8}}=2^{\frac{32}{8}+\frac{15}{8}}=2^{\frac{47}{8}}$ this one?

55. King

no how did u take 2^15/4 out frm sqrt

56. Ishaan94

http://www.wolframalpha.com/input/?i=log_4%28%2832+*+%2816+*%2864+*+8^%28-3%2F4%29%29^%281%2F2%29%29^%281%2F3%29%29^%281%2F4%29 Tomas Is Right, FIITJEE is wrong!

57. King

ok now can u xplain

58. Tomas.A

$\sqrt{2^\frac{15}{4}}=2^{\frac{15}{4}\cdot\frac{1}{2}}=2^\frac{15}{8}$

59. King

oh right

60. Tomas.A

$\sqrt[n]{m}=m^{\frac{1}{n}}$

61. King

Yipppeeeeeeeee u guys are great!!!!!!!!!! thnx to all of u.!!!!!!!!!!!!!!!