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Math Help - solving this with ln

  1. #1
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    solving this with ln

    A bit rusty on the ln's.

    1.5=ke^3k.

    attempt

    ln1.5=3klne

    ln1.5=3k(1)

    (ln1.5)/3=k???

    Thanks....
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  2. #2
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    Re: solving this with ln

    Quote Originally Posted by Neverquit View Post
    A bit rusty on the ln's.

    1.5=ke^3k.

    attempt

    ln1.5=3klne

    ln1.5=3k(1)

    (ln1.5)/3=k???

    Thanks....
    you have k as a coefficient of the exponential term and k as part of the exponent. An elementary algebraic approach to solve for k is not available ... you'll need to use technology.

    let k = x

    graph y = xe^{3x} - 1.5 and locate any zeros ...

    x = k = 0.4224126...
    Thanks from Neverquit
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  3. #3
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    Re: solving this with ln

    Quote Originally Posted by Neverquit View Post
    A bit rusty on the ln's.

    1.5=ke^3k.

    attempt

    ln1.5=3klne

    ln1.5=3k(1)

    (ln1.5)/3=k???

    Thanks....
    I will assume that equation is :

     1.5=k\cdot e^{3k}

     4.5 = 3k \cdot e^{3k} \Rightarrow 3k=W(4.5) \Rightarrow k=\frac{W(4.5)}{3}

    where ~W~ is Lambert W function .
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