## UnknownRandom one year ago Could somebody help me with this log problem?

1. cutiecomittee123

what is it

2. UnknownRandom

4log4(3)-log4(4)

3. UnknownRandom

The answer can't contain a log

4. cutiecomittee123

I am really rusty and logs because I havent done them in a year or so. But I think you have to convert it to a diferent form inorder to solve it

5. Nnesha

familiar with the log properties ?

6. UnknownRandom

Yep.

7. Nnesha

8. UnknownRandom

log4(81/4)?

9. Nnesha

looks good

10. Nnesha

now set it equal to x or use change of base formula

11. Nnesha

if we set it equal to x we should change log to exponential form

12. UnknownRandom

I can't remember how to do that.

13. Nnesha

for change of base formula $\huge\rm log_b a = \frac{ \log a }{ \log b }$

14. Nnesha

and if you want to do it by hands so set it equal to x |dw:1443129484346:dw|

15. UnknownRandom

|dw:1443129612389:dw|

16. UnknownRandom

Is that right?

17. UnknownRandom

Solving for that power?

18. Nnesha

yes let missing exponent equal to x and then write 81 in terms of base 4

19. Nnesha

4 to the what power =81?

20. UnknownRandom

Wait, why can you cancel that 4?

21. UnknownRandom

in 81/4

22. Nnesha

how would you cancel it ?

23. UnknownRandom

How did you get rid of that 4 in 81/4?

24. Nnesha

we should rewrite 81 in terms of base 4 so we can apply the exponent rule $\huge\rm \frac{ x^m }{ x^n }=x^{m-n}$

25. Nnesha

we need 4 base at the numerator so rewrite 81 in terms of base 4 4 to the what power = 81 ?

26. Nnesha

alright wait a sec

27. Nnesha

ahh i see we can't write 81 in terms of base 4 3^4 = 81 i was thinking 4^3 sorry about that

28. Nnesha

well u have to take log to solve for x so jsut use change of base formula that would be easy

29. UnknownRandom

30. Nnesha

change of base formula

31. UnknownRandom

How do write that?

32. UnknownRandom

*you

33. Nnesha

$\huge\rm \log_\color{blue}{b} \color{ReD}{a} =\frac{ \log\color{red}{ a} }{ \log \color{blue}{b} }$

34. UnknownRandom

log (81/4)/log(4)?

35. Nnesha

good right!!

36. UnknownRandom

Do you subtract the two now?

37. Nnesha

subtract no just divide them we don't need the original question

38. UnknownRandom

True, but on our test we can't use calculators so I don't know how I would do that division without one.

39. Nnesha

can't use calculator hm i mean not just for log(4) ???

40. UnknownRandom

41. Nnesha

we have to use calculator for this one bec 81/ 4 is a decimal answer u were asking can we multiply 4 both sides ? yes you can |dw:1443130983953:dw|

42. Nnesha

when we multiply same bases we should add exponents $\huge\rm x^m \times x^n=x^{m+n}$ $\large\rm 4^1 \times 4^x =81 ~~~~~~~~~~4^{1+x}=81$

43. UnknownRandom

So how do you find x?

44. Nnesha

now take log both sides to move the exponent at front $\huge\rm (1+x )\log(4) = \log (81)$ now u can solve for x

45. Nnesha

divide both sides by log(4) and then subtract 1

46. UnknownRandom

Ok, I got 2.169925001 but it said the answer was wrong.

47. Nnesha

48. Nnesha

is there any statement round some hundred/thousandth ?

49. UnknownRandom

Nope

50. Nnesha

well i round it hundred place 2.169925001 (two numbers after decimal if the the 3rd is 5 or greater than 5 then we can wround to 7) 2.169925001 hundredths place 2.17

51. Nnesha

did they gave u the right answer ?

52. UnknownRandom

Nope :(

53. Nnesha

ugh that's what i got and that's exactly what on this calc http://www.wolframalpha.com/input/?i=4log4%283%29-log4%284%29

54. UnknownRandom

I don't know then. Thanks for the help though.

55. Nnesha

alright ask ur teacher let me know what 's the correct answer if that's not right good luck!

56. UnknownRandom

I just typed 3/4 and it worked. Wow.... I guess the 4 wasn't supposed to be there on that problem. @Nnesha

57. Nnesha

3/4 ? what 4 wasn't supposed to be there ?

58. UnknownRandom

I guess not. Somebody done messed up.

59. UnknownRandom

and wasted 2 hours of my life.

60. Nnesha

i don't get it so what was the question ?

61. UnknownRandom

The question was evaluate 4*log4(3)-log4(4)

62. Nnesha

so 4 isn't a base ?

63. Nnesha

$4 \log4(3) - \log4(4)$ like this or $4\log_4 (3) - \log_4(4)$

64. UnknownRandom

The second one

65. Nnesha

okay there is 4 at front of log so we have to apply the power rule right

66. UnknownRandom

Yep

67. Nnesha

so $\log_4 (3)^4 - \log_4 4 = \log_4 \frac{ (3)^4 }{ 4 }$ that's what we did so what was the mistake ? o.O hmm

68. UnknownRandom

I think it was typed wrong and the 4 in the front shouldn't have been there.

69. Nnesha

oh okay so $\large\rm \log_4 \frac{ 3 }{ 4 }$

70. UnknownRandom

That's what I think.

71. Nnesha

that will give u the negative answer

72. Nnesha

we can just guess if we don't know what the question is exly

73. UnknownRandom

$4\log_4{3}-1$

74. UnknownRandom

So $\frac{ \log3 }{ \log4 }-1$

75. UnknownRandom

= -.208

76. UnknownRandom

4^-.208 = 3/4

77. UnknownRandom

@Nnesha

78. UnknownRandom

4^log4(3)-log4(4) That is what the problem was supposed to say.

79. Nnesha

take a screenshot plz you're not sure abt the question ..