Solve for x over the real numbers:
e^(-x)+e^x = 8 (e^x-e^(-x))
8 (e^x-e^(-x)) = 8 e^x-8 e^(-x):
e^(-x)+e^x = 8 e^x-8 e^(-x)
Multiply both sides by e^x:
1+e^(2 x) = 8 e^(2 x)-8
Subtract 1+8 e^(2 x) from both sides:
-7 e^(2 x) = -9
Divide both sides by -7:
e^(2 x) = 9/7
Take the natural logarithm of both sides:
2 x = log(9/7)
Divide both sides by 2:
Answer: |x = 1/2 log(9/7)
