Question

e^x + e^2x = e^3x
how to solve this ?=[

Answer 1

\[e ^{x} + e ^{2x} = e ^{3x}\]

Answer 2

start by substitution
w+w^2-w^3=0
w(1+w-w^2)=0

Answer 3

let u=e^x
u+u^2-u^3=0
u(1 + u - u^2)=0

u=0
and solve that quadratic using the quadratic formula.
don't forget to back substitute and solve for x.

Answer 4

oh !

Answer 5

thank you guys ~!!

Answer 6

\[e^x +e^{2x} =e^{3x}\]\[e^x +e^{2x} -e^{3x}=0\]\[e^x(1 +e^{x} -e^{2x})=0\]\[e^x=0(rejected) \ or\ (1 +e^{x} -e^{2x})=0\]\[ (1 +e^{x} -e^{2x})=0\]\[e^x = \frac{-1 \pm \sqrt{(1)^2 -4(-1)(1)}}{2(-1)}\] .... Can you do it?

Answer 7

that one is better ^^^