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Solve an exponential equation

  1. Jun 16, 2016 #1

    Rectifier

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    The problem
    Solve ## e^x-e^{-x} = 6 ## .

    The attempt
    $$ e^x-e^{-x} = 6 \\ e^x(1-e^{-1}) = 6 \\ e^x = \frac{6}{(1-e^{-1})} \\ x = \ln \left( \frac{6}{1-e^{-1}} \right) \\ $$

    The answer in the book is ## \ln(3 + \sqrt{10})##

    Could someone help me?
     
  2. jcsd
  3. Jun 16, 2016 #2

    Rectifier

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    I made a mistake at the second step ## e^{-x} \neq e^{-1} \cdot e^x ##
     
  4. Jun 16, 2016 #3

    Math_QED

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    Make the substitution y = e^x.
     
  5. Jun 16, 2016 #4

    Ray Vickson

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    Right: ##e^{-x} = \frac{1}{e^x}##.
     
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