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Math Help - Solve for x using Log

  1. #1
    Zel
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    Question Solve for x using Log

    (2^-x)sinx = 1/2x - 1
    My teacher said to use logs, but I'm useless at them
    I would really appreaciate any help given
    Thanks in advance!
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  2. #2
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    Quote Originally Posted by Zel View Post
    (2^-x)sinx = 1/2x - 1
    My teacher said to use logs, but I'm useless at them
    I would really appreaciate any help given
    Thanks in advance!
    Having two different transcendental functions makes that a really difficult equation, particularly with that (1/2)x- 1. Unless you mean (1/2)^x= 2^{-x}[/tex]. If so, it is still difficult but you might be able to write sin(x) as \frac{e^{ix}- e^{-ix}}{2i} and write 2^{-x} as e^{-xln(2)}
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Zel View Post
    (2^-x)sinx = 1/2x - 1
    My teacher said to use logs, but I'm useless at them
    I would really appreaciate any help given
    Thanks in advance!
    Can you add some brackets to make it clear if the right hand side is:

    \frac{1}{2x-1}

    \frac{1}{2}x -1

    \frac{1}{2x}-1

    or whatever?

    I also doubt that this can be rearranged as required.

    CB
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by HallsofIvy View Post
    Having two different transcendental functions makes that a really difficult equation, particularly with that (1/2)x- 1. Unless you mean (1/2)^x= 2^{-x}[/tex]. If so, it is still difficult but you might be able to write sin(x) as \frac{e^{ix}- e^{-ix}}{2i} and write 2^{-x} as e^{-xln(2)}
    The mixture of exponential and linear functions of x still means this is likely to involve our old favourite, Lambert's W.

    CB
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