Question

solve e^2x-5e^x+6=0

Answer 1

And show and explain the steps

Answer 2

let us do a substitution and see if you can then solve it.

Let \(y=e^x\), then what you have is \(y^2-5y+6=0\)

Can you solve for \(y\)?

Answer 3

No I'm solving for x......I think it has something to do with letting e^x = u

Answer 4

ok then replace my y with u

Answer 5

\(\large\tt \begin{align} \color{black}{e^{2x}-5e^x+6=0\\~\\
(e^{x})^2-5(e^x)+6=0\\~\\
\text{put e^x=y}\\~\\
y^2-5y+6=0\\~\\
y^2-2y-3y+6=0\\~\\
y(y-2)-3(y-2)=0\\~\\
(y-3)(y-2)=0\\~\\
y=3~~or~~y=2\\~\\
e^{x}=3~~or~~e^{x}=2\\~\\
ln(e^{x})=ln3~~or~~ln(e^{x})=ln2\\~\\
xln(e)=ln3~~or~~xln(e)=ln2\\~\\
x=ln3~~or~~x=ln2\\~\\

}\end{align}\)

Answer 6

like that^^^

Answer 7

we do not have to use \(u\), we can use \(y,c,a,v,f,g,t,....\) what ever we want

Answer 8

\(\text{note that ln(e)=1}\\~\\\)

Answer 9

Got it!!!!!!! Thanks guys