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Math Help - [SOLVED] Find equation of y in terms of x?

  1. #1
    Super Member fardeen_gen's Avatar
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    [SOLVED] Find equation of y in terms of x?

    If x = e^3t & y = e^t, where e is exponential number

    Find equation of y in terms of x?
    Ans: y^3 = 3x

    These are my steps:
    x = e^3t
    (or) e^(ln x) = e^3t
    (or) ln x = 3t
    (or) t = (ln x)/3 ------(i)

    y = e^t
    (or) e^(ln y) = e^t
    (or) ln y = t
    (or) ln y = (ln x)/3 ------Using (i)

    What to do after this???

    ~~~~~~~~~~~~~~~~~~~
    EDIT: Question NULL & VOID
    Last edited by fardeen_gen; August 27th 2008 at 06:36 AM.
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  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
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    P(I'm here)=1/3, P(I'm there)=t+1/3
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    Hello,

    That's pretty weird... Is it x=e^{3t} and y=e^t ?

    If so, then remember this property : a^{bc}=(a^b)^c=(a^c)^b

    Therefore x=e^{3t}=(e^t)^3=y^3
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  3. #3
    Super Member fardeen_gen's Avatar
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    Hello Moo.
    The original question was a mechanics question. It stated:
    A body starts from origin with velocity V = (e^3t)i + (e^t)j. Then find the equation of trajectory of the body?

    Ans: y^3 = 3x
    i - unit vector along x-axis
    j - unit vector along y-axis
    Was my interpretation of the question wrong?

    EDIT: I messed up. dx/dt = e^3t and dy/dt = e^t.
    Which gives x = e^(3t)/3 and y = e^t
    And using the obvious property which Moo stated(instead of doing the rubbish I did by taking natural log), x = (y^3)/3
    Last edited by fardeen_gen; August 27th 2008 at 06:41 AM.
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