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Math Help - indicial equation

  1. #1
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    indicial equation

    I can't seem to solve this:

    3x = 10^-0.3x

    All I do is go around in circles
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  2. #2
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    Quote Originally Posted by freswood
    I can't seem to solve this:

    3x = 10^-0.3x

    All I do is go around in circles
    Is your problem I presume,
    3x=10^{.3x}
    Let, y=.3x
    Then,
    10y=3x
    Thus,
    10y=10^{y}
    Thus,
    y=10^{y-1}
    We can see that y=1 is a solution because,
    1=10^{1-1}=10^0=1
    Thus,
    .3x=1
    thus,
    x=\frac{10}{3}
    ------------------
    Though I did not prove it, I believe there are no other solutions because this leads to the Lambert function, but I do not know if this is a high school problem or a problem for Analysis class which your professor want to demonstrate with the Lambert function. If a high school function igonore this entire paragraph.
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  3. #3
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    Ta heaps.

    Ugh why didn't I think of that?? I can be such an idiot sometimes.
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  4. #4
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    Quote Originally Posted by freswood
    Ugh why didn't I think of that??
    Maybe because you do not pay attention is class but fool around with you palm pilot and play games
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  5. #5
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    Quote Originally Posted by ThePerfectHacker
    Maybe because you do not pay attention is class but fool around with you palm pilot and play games


    Maybe it's because I'm not a very lateral thinker and this is the best I can do
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by ThePerfectHacker
    Is your problem I presume,
    3x=10^{.3x}
    Let, y=.3x

    [snip]

    ------------------
    Though I did not prove it, I believe there are no other solutions because this leads to the Lambert function, but I do not know if this is a high school problem or a problem for Analysis class which your professor want to demonstrate with the Lambert function. If a high school function igonore this entire paragraph.

    the function:

    <br />
f(x)=10^{0.3x}-3x<br />

    is increasing on (-\infty,\infty) so any real root will be unique.

    RonL
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