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Math Help - Exponential Equation

  1. #1
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    Exponential Equation

    Please help. I have not had algebra for thirty years. How do you solve the following equation?

    2^x=2x

    Thanks for the help!
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  2. #2
    Junior Member enjam's Avatar
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    2^x = 2x
    ln(2^x) = ln(2x)
    xln(2) = ln(2) + ln (x)
    x = [ln (2) + ln (x)] / ln (2)
    x = 1 + ln(x)/ln(2)

    From here, by simple inspection, we can see that x can be either 1 or 2.
    when x = 1, we have 1 = 1 + ln(1)/ln(2) = 1 + 0
    when x = 2, we have 2 = 1 + ln(2)/ln(2) = 1 + 1
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  3. #3
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    Thanks for your response. Other than by inspection, is there a way to solve a more generic equation. For example, solve for x when a^x=bx.
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  4. #4
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    e^(i*pi)'s Avatar
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    There are iterative methods but none analytical ones
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