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Math Help - Is there a way to further reduce this?

  1. #1
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    Is there a way to further reduce this?

    ln(y)=(2/3)*ln(x)

    thanks
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  2. #2
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    Question

    I am guessing that the text in the subject line is your question...?

    What do you mean by "reducing" the equation?
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  3. #3
    Junior Member enjam's Avatar
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    ln(y)=(2/3)*ln(x)
    = ln(y) = ln(x)^(2/3)
    Multiplying both sides by e, we end up with:
    y = x^(2/3)
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  4. #4
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    thanks enjam, that's just what i was confused about. i didn't know that e^2/3lnx = x^2/3

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  5. #5
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    Quote Originally Posted by enjam View Post
    Multiplying both sides by e, we end up with:
    y = x^(2/3)
    Actually, no. If you multiply through by a constant, you will end up with the same logarithmic equation, but now multiplied through by a constant.

    Instead, you need to raise both sides of the equation as powers on the base e.

    Quote Originally Posted by PandaNomium View Post
    i didn't know that e^2/3lnx = x^2/3
    There's a good reason for not having know that: it's not true!

    However, e^ln(x^(2/3)) does equal x^(2/3).
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  6. #6
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    so what would be the simplified version of: e^(2/3lnx)
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  7. #7
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    Quote Originally Posted by PandaNomium View Post
    so what would be the simplified version of: e^(2/3lnx)
    HI

    e^[(2/3)lnx] would be x^(2/3)
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  8. #8
    Senior Member pacman's Avatar
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    property of logarithm: p(ln x) = ln (x)^p

    ln(y)=(2/3)*ln(x) = ln (x)^(2/3)

    raise BS to e,

    e^( ln y) = e^(ln (x)^(2/3))

    but by definition, e^(ln y) = y, then

    y = x^(2/3)

    if you want a graph, see below.
    Attached Thumbnails Attached Thumbnails Is there a way to further reduce this?-k.gif  
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