exponential equation
posted by Tiffany on .
Solve the exponential equation
e^x + e^x = 6

let e^x = a
then we have
a + 1/a = 6
a^2 + 1  6a = 0
a^2  6a = 1
completing the square, (in this case faster than using the formula)
a^2  6a + 9 = 1 + 9
(a3)^2 = 8
a3 = ± √8
a = 3± 2√2
so e^x = 3 + √8 OR e^x = 3  √8
using my calculator
x = ln(3+√8) = 1.7627.. or
x = ln(3√8) = 1.7627..