Question

how do you solve e^(2x) − 4e^x + 3 = 0

Answer 1

its just a quadratic in disguise

Answer 2

let u = e^x; x = ln(u)

u^2 -4u +3 = 0

once you know u, you know x

Answer 3

why is x= ln (u) ?

Answer 4

@amistre64

Answer 5

its a substitution
\[(e^x)^2=e^{2x}\]
since e^x is just "some unknown value", it is a variable

let u = e^x

when we know the value of u, say its 5

5 = e^x , we still need to solve for x; ln(u) = x

Answer 6

im assuming you know what an inverse function is.

Answer 7

e^x = y, if and only if, x = ln(y)

if you do not know this relation yet, then it would take a bit of explaining to prove :)

Answer 8

thanks I get it :)

Answer 9

@amistre64

Answer 10

howdy