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Log question

  1. Oct 30, 2005 #1
    Hi, this should be the last question for today :lol:
    Determine the number of solutions for the following system:
    [tex] y = -4log_{12} (x) [/tex]
    [tex] y = 4 sin(x) [/tex]
    Is there a way to do this without using a graphing calculator? Thank you very much!
     
    Last edited: Oct 30, 2005
  2. jcsd
  3. Oct 30, 2005 #2

    Tide

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    You do know that -1 <= sin(x) <= 1. That should be a good place to start. :)
     
  4. Oct 31, 2005 #3
    Hi, hopefully you know some properties of log for the first one.
    Hint:[tex]y=log_{10}(x)[/tex]
    [tex]10^y = x[/tex]
    and [tex]y=a*logx = log(x^a)[/tex]

    For the second one, what do you have trouble with?
    Can you draw [tex]y=sinx[/tex]?(of course without a calculator)
    If you CAN, 4 is just the amplitude, and the graph's domain is[tex](-\infty, \infty)[/tex]
     
  5. Oct 31, 2005 #4
    Thanks for the input, but that's how far I got by myself :(
    I should I get the intersecting points of the two graphs? Should I just use the calculator? Or is there another way around it?
     
  6. Oct 31, 2005 #5
    You don't need to "get the intersecting points of the two graphs", you want to find their number.
    Helpful apprach - solve an easier problem first:
    how many points of intersection do these graphs have
    [tex]y=4 sin(x)[/tex] and
    [tex]y=x / 25[/tex] ?
    Graph "by hand" and see the pattern.
     
    Last edited: Oct 31, 2005
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