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Solve an exponential equation

  • #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?
 

Answers and Replies

  • #2
Rectifier
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313
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I made a mistake at the second step ## e^{-x} \neq e^{-1} \cdot e^x ##
 
  • #3
Math_QED
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I made a mistake at the second step ## e^{-x} \neq e^{-1} \cdot e^x ##
Make the substitution y = e^x.
 
  • #4
Ray Vickson
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I made a mistake at the second step ## e^{-x} \neq e^{-1} \cdot e^x ##
Right: ##e^{-x} = \frac{1}{e^x}##.
 

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