a. (1/2) ln 2
b. (1/3) ln 2
c. (1/3) ln 3
d. (1/2) ln 3
e. ln 2
f. ln 3
g. none of these
2007-12-15 16:19:37 · 3 answers · asked by ace 1 in Science & Mathematics ➔ Mathematics
The answer is (f), ln 3. The easiest way to see this is to substitute the answer into your equation:
Exp(ln 3) + 9 Exp(- ln3) = 3 +9/3 = 6
Since Exp and ln are inverse functions, Exp(ln x) = x, so Exp (ln 3) = 3.
Since Exp (-x) = 1/Exp(x), we can write 9 Exp(-x) = 9/Exp(x), so if x = ln 3, 9 Exp(-ln3) = 9/Exp(ln 3)=9/3=3.
2007-12-15 16:30:07 · answer #1 · answered by kuiperbelt2003 7 · 0⤊ 0⤋
e^x + 9/e^x = 6
e^2x - 6e^x + 9 = 0
(e^x - 3)^2 = 0
e^x = 3
x = ln 3
2007-12-15 16:31:37 · answer #2 · answered by norman 7 · 0⤊ 0⤋
ex + 9e-x = 6
ex - x = 6 - 9e
x (e-1) = 6-9e
x = (6 - 9e)/(e - 1)
2007-12-15 16:32:14 · answer #3 · answered by Enzo H 1 · 0⤊ 0⤋