# Solve an exponential equation

Gold Member
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?

Gold Member
I made a mistake at the second step ## e^{-x} \neq e^{-1} \cdot e^x ##

member 587159
I made a mistake at the second step ## e^{-x} \neq e^{-1} \cdot e^x ##

Make the substitution y = e^x.

Ray Vickson