how would you solve for x: (e^(x)+e(-x)/2)=3

Answer 1

let y = e^x
then (e^(x)+e(-x)/2)=3 is
y + 1/(2y) = 3
2y^2 - 6y + 1 = 0
by quadratic formula
y = 2.8229 or y = .17712
then
e^x = 2.8229
x = ln(2.8229) = 1.037756

or

e^x = .17712
x = ln(.17712) = -1.7309