precal
posted by ladybug on .
solve the equation algebraically.
7e^x=11e^x

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...