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Egative power indicates an inverse

  1. Sep 15, 2005 #1
    Why is 3^x > e^x > 2^x when x>0, but 3^x < e^x < 2^x when x<0???
     
  2. jcsd
  3. Sep 15, 2005 #2
    e is approx. 2.72

    so 3^1=3
    2.72^1=2.72
    2^1=2

    therefore 3^x>e^x>2^x when x>0

    however, when you get into the negatives

    3^-1=1/3
    2.72^-1=1/2.72
    2^-1=1/2


    this is because a negative power indicates an inverse( 1/x ), so the smaller the number with a negative power, the smaller the denomenator will be
     
  4. Sep 15, 2005 #3

    EnumaElish

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    Another way of looking at it. Since 3 > e and therefore Log(3) > 1, x Log(3) > x implies x > 0 and x Log(3) < x implies x < 0.
     
  5. Sep 17, 2005 #4

    HallsofIvy

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    All this is saying is that if 0<a< b< c then 0< 1/c< 1/b< 1/a

    If a< b and a and b are positive, then 1< b/a because we have divided by a positive number.

    Then 1/b< 1/a because we have divided by a positive number.
     
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