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UnknownRandom

  • one year ago

Could somebody help me with this log problem?

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  1. cutiecomittee123
    • one year ago
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    what is it

  2. UnknownRandom
    • one year ago
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    4log4(3)-log4(4)

  3. UnknownRandom
    • one year ago
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    The answer can't contain a log

  4. cutiecomittee123
    • one year ago
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    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
    • one year ago
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    familiar with the log properties ?

  6. UnknownRandom
    • one year ago
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    Yep.

  7. Nnesha
    • one year ago
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    alright apply log property start with the power rule

  8. UnknownRandom
    • one year ago
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    log4(81/4)?

  9. Nnesha
    • one year ago
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    looks good

  10. Nnesha
    • one year ago
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    now set it equal to x or use change of base formula

  11. Nnesha
    • one year ago
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    if we set it equal to x we should change log to exponential form

  12. UnknownRandom
    • one year ago
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    I can't remember how to do that.

  13. Nnesha
    • one year ago
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    for change of base formula \[\huge\rm log_b a = \frac{ \log a }{ \log b }\]

  14. Nnesha
    • one year ago
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    and if you want to do it by hands so set it equal to x |dw:1443129484346:dw|

  15. UnknownRandom
    • one year ago
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    |dw:1443129612389:dw|

  16. UnknownRandom
    • one year ago
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    Is that right?

  17. UnknownRandom
    • one year ago
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    Solving for that power?

  18. Nnesha
    • one year ago
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    yes let missing exponent equal to x and then write 81 in terms of base 4

  19. Nnesha
    • one year ago
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    4 to the what power =81?

  20. UnknownRandom
    • one year ago
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    Wait, why can you cancel that 4?

  21. UnknownRandom
    • one year ago
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    in 81/4

  22. Nnesha
    • one year ago
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    how would you cancel it ?

  23. UnknownRandom
    • one year ago
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    How did you get rid of that 4 in 81/4?

  24. Nnesha
    • one year ago
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    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
    • one year ago
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    we need 4 base at the numerator so rewrite 81 in terms of base 4 4 to the what power = 81 ?

  26. Nnesha
    • one year ago
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    alright wait a sec

  27. Nnesha
    • one year ago
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    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
    • one year ago
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    well u have to take log to solve for x so jsut use change of base formula that would be easy

  29. UnknownRandom
    • one year ago
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    I was lost. The application we use to answer questions won't take answers with log in it. So what do you recommend?

  30. Nnesha
    • one year ago
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    change of base formula

  31. UnknownRandom
    • one year ago
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    How do write that?

  32. UnknownRandom
    • one year ago
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    *you

  33. Nnesha
    • one year ago
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    \[\huge\rm \log_\color{blue}{b} \color{ReD}{a} =\frac{ \log\color{red}{ a} }{ \log \color{blue}{b} }\]

  34. UnknownRandom
    • one year ago
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    log (81/4)/log(4)?

  35. Nnesha
    • one year ago
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    good right!!

  36. UnknownRandom
    • one year ago
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    Do you subtract the two now?

  37. Nnesha
    • one year ago
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    subtract no just divide them we don't need the original question

  38. UnknownRandom
    • one year ago
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    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
    • one year ago
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    can't use calculator hm i mean not just for log(4) ???

  40. UnknownRandom
    • one year ago
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    Nope, but we will probably be able to use log in our answers on the test.

  41. Nnesha
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    So how do you find x?

  44. Nnesha
    • one year ago
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    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
    • one year ago
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    divide both sides by log(4) and then subtract 1

  46. UnknownRandom
    • one year ago
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    Ok, I got 2.169925001 but it said the answer was wrong.

  47. Nnesha
    • one year ago
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    http://www.wolframalpha.com/input/?i=4log4%283%29-log4%284%29 that's the correct answer

  48. Nnesha
    • one year ago
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    is there any statement round some hundred/thousandth ?

  49. UnknownRandom
    • one year ago
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    Nope

  50. Nnesha
    • one year ago
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    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
    • one year ago
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    did they gave u the right answer ?

  52. UnknownRandom
    • one year ago
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    Nope :(

  53. Nnesha
    • one year ago
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    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
    • one year ago
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    I don't know then. Thanks for the help though.

  55. Nnesha
    • one year ago
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    alright ask ur teacher let me know what 's the correct answer if that's not right good luck!

  56. UnknownRandom
    • one year ago
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    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
    • one year ago
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    3/4 ? what 4 wasn't supposed to be there ?

  58. UnknownRandom
    • one year ago
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    I guess not. Somebody done messed up.

  59. UnknownRandom
    • one year ago
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    and wasted 2 hours of my life.

  60. Nnesha
    • one year ago
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    i don't get it so what was the question ?

  61. UnknownRandom
    • one year ago
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    The question was evaluate 4*log4(3)-log4(4)

  62. Nnesha
    • one year ago
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    so 4 isn't a base ?

  63. Nnesha
    • one year ago
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    \[4 \log4(3) - \log4(4)\] like this or \[4\log_4 (3) - \log_4(4)\]

  64. UnknownRandom
    • one year ago
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    The second one

  65. Nnesha
    • one year ago
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    okay there is 4 at front of log so we have to apply the power rule right

  66. UnknownRandom
    • one year ago
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    Yep

  67. Nnesha
    • one year ago
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    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
    • one year ago
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    I think it was typed wrong and the 4 in the front shouldn't have been there.

  69. Nnesha
    • one year ago
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    oh okay so \[\large\rm \log_4 \frac{ 3 }{ 4 }\]

  70. UnknownRandom
    • one year ago
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    That's what I think.

  71. Nnesha
    • one year ago
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    that will give u the negative answer

  72. Nnesha
    • one year ago
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    we can just guess if we don't know what the question is exly

  73. UnknownRandom
    • one year ago
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    \[4\log_4{3}-1 \]

  74. UnknownRandom
    • one year ago
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    So \[\frac{ \log3 }{ \log4 }-1\]

  75. UnknownRandom
    • one year ago
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    = -.208

  76. UnknownRandom
    • one year ago
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    4^-.208 = 3/4

  77. UnknownRandom
    • one year ago
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    @Nnesha

  78. UnknownRandom
    • one year ago
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    4^log4(3)-log4(4) That is what the problem was supposed to say.

  79. Nnesha
    • one year ago
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    take a screenshot plz you're not sure abt the question ..

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