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CALC AB problems

  1. Apr 14, 2009 #1

    coookiemonste

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    1. The problem statement, all variables and given/known data
    Let f be the functions f(x)=ln(3x+2)^k for some positibe constant k.
    If f'(2)=3, what is the value of k?
    the answer is 8,but i dont think i am taking the derivative right.



    2. Relevant equations
    ?


    3. The attempt at a solution
    f'(x)=3k*ln(3x+2)^(k-1)/(3x+2)
    then i plugged in (2,3) into the derivative above.
    and i got k=8/(ln8)(8^(k-1))
     
    coookiemonste, Apr 14, 2009
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  3. Apr 14, 2009 #2

    Pengwuino

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    Gold Member

    The derivative is correct, but the answer is not 8. If you plug in (2,3) into your derivative with k=8, you will get a contradiction.
     
    Pengwuino, Apr 14, 2009
  4. Apr 15, 2009 #3

    coookiemonste

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    my ap book says the answer is 8, however it may be wrong.
    but how would you find the value of k?
    i am not allowed to use a calculator with this problem.
     
    coookiemonste, Apr 15, 2009
  5. Apr 15, 2009 #4

    rock.freak667

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    Homework Helper

    try using the fact that

    [tex]log_a b^r=rlog_a b[/tex]
     
    rock.freak667, Apr 15, 2009
  6. Apr 15, 2009 #5

    coookiemonste

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    AH!
    thank you!
     
    coookiemonste, Apr 15, 2009
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