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Homework Help: Basic Calculus- Please help

  1. Jun 18, 2011 #1
    1. The problem statement, all variables and given/known data

    If sinx(lnx)=0 over [0, 2pi] then x=_____



    3. The attempt at a solution

    My attempt was to move sin over to the other side to get lnx= 0/sinx and then get lnx=0, making x=1. But is it incorrect to just move sinx over to the other side, because if i move lnx over to the other side, i would get x=0. Can you please explain to me what I am doing wrong here?
     
  2. jcsd
  3. Jun 18, 2011 #2
    Well, if those are factors; Sin(x) and ln(x). Then there are 4 solutions. You found ln(1)=0 then you just need to find those values that makes Sin(x)=0, one of the solutions are not legit since they are not defined by ln(x)

    The question has nothing to do with calculus though :P
     
    Last edited: Jun 18, 2011
  4. Jun 18, 2011 #3
    how do you know there are 4 solutions?
    and yes, this is just our summer review to go into calc. lol
     
  5. Jun 18, 2011 #4

    eumyang

    User Avatar
    Homework Helper

    Then you should have posted this in the Precalculus subforum instead. :tongue:

    There are 3 solutions because,
    there is 1 solution in [0, 2π] where ln x = 0, and
    there are 2 solutions in [0, 2π] where sin x = 0 (a 3rd is not in the domain of the ln x function).
     
    Last edited: Jun 18, 2011
  6. Jun 18, 2011 #5

    Mark44

    Staff: Mentor

    I get 3 solutions. One of the 3 solutions in [0, 2π] for which sin x = 0 is not in the domain of the ln function.
     
  7. Jun 18, 2011 #6
    You can't really just move the sine over like that. Sin is an operator! What you need to do is consider what would make sin(something) = 0. (consult your unit circle). Once you have those 2 solutions, set the argument of the sin to that.
    ln(x) = solution 1
    ln(x) = solution 2
    etc.
     
  8. Jun 18, 2011 #7

    Mark44

    Staff: Mentor

    QuarkCharmer, you're misreading the problem, which is understandable due to the way the OP wrote the problem. Howebver, the expression on the left is a product, not a composition. It's sin(x) * ln(x), not sin(ln(x)).
     
  9. Jun 18, 2011 #8
    My mistake, feel free to delete my post(s)
     
  10. Jun 18, 2011 #9

    eumyang

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    Homework Helper

    Ack, that's what I get for blinding following someone else's post. :redface: Post corrected.
     
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