solve the equation algebraically.

Question

7e^x=11-e^-x

Answer 1

7 e^x = 11 - 1/e^x

let e^x = t

7t = 11 - 1/t
times t
7t^2 = 11t - 1
7t^2 - 11t + 1 = 0
t = (11 ± √93)/14

then e^x = (11 + √93)/14 = 1.474546...
x = ln 1.4745.. = .38835..

or

e^x = (11 - √93)/14 = .096882..
x = ln .096882.. = -2.33426...