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Math Help - exponential equations

  1. #1
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    exponential equations

    I'd appreicate any assistance in answering this questionHeadbang)
    3^x+1=6^x-1. The answer needs to be rounded to three decimal places. Thanks in advance.
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  2. #2
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    I assume the equation is 3^{x + 1} = 6^{x - 1}<br />
    Take logs:

    (x + 1) \log 3 = (x - 1) \log 6

    Rearrange:

    \frac{x + 1}{x - 1} = \frac{\log 6}{\log 3}

    \frac{x - 1}{x - 1} + \frac{2}{x - 1} = \frac{\log 6}{\log 3}

    1 + \frac{2}{x - 1} = \frac{\log 6}{\log 3}

    \frac{2}{x - 1} = \frac{\log 6}{\log 3} - 1

    Can you solve it now?
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  3. #3
    Math Engineering Student
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    \begin{aligned}<br />
   3^{x+1}&=6^{x-1} \\ <br />
  3^{x}\cdot 3&=\frac{6^{x}}{6} \\ <br />
  2^{x}&=18 \\ <br />
  x\log 2&=\log 18 \\ <br />
  x&=\frac{\log 18}{\log 2}.<br />
\end{aligned}
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