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Math Help - zeros

  1. #1
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    zeros

    How many zeros does the function y = sin(lnx) have for 0<x<1 ?
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    Quote Originally Posted by DINOCALC09 View Post
    How many zeros does the function y = sin(lnx) have for 0<x<1 ?
    \sin (\ln x) = 0 \implies \ln x = \pi n \mbox{ where }n\in \mathbb{Z}. Thus, x = e^{\pi n} if n=-1,-2,-3,... then  0 < x < 1 and it is a zero. Thus, there are infinitely many zeros.
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  3. #3
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    Hello,

    You know that if 0<x<1, ln(x)<0

    But within ]- \infty;0[ there is an infinity of solutions making sin(ln(x))=0, because of the 2pi period.
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  4. #4
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    Quote Originally Posted by DINOCALC09 View Post
    How many zeros does the function y = sin(lnx) have for 0<x<1 ?
    \sin(\ln|x|)=0

    \ln|x| = \sinh(0) \Rightarrow \ldots -\pi, 0, \pi \ldots

    x = e^{\pi n} for n \ge 0 where n is an integer and 0 < x < 1

    Therefore \pi n < 0, so n < 0

    x = e^{\pi n}  \forall n < 0, n \in Z

    \forall: for all* (isn't this supposed to have a horizontal line through the middle?)

    However....
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  5. #5
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    Write "\forall" in the math tags :-)
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  6. #6
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    Quote Originally Posted by Moo View Post
    Write "\forall" in the math tags :-)
    Thanks!
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