Question

Can someone show me how to do this please. I am stuck.


find a number x such that
e^2x – 12e^x =13

Answer 1

Substitute y=e^x to get a quadratic equation:
y²-12x+13=0
Solve for y.
Substitute the values of y=e^x into the original equation to make sure that all the roots are feasible/defined.
See also previous example:
http://www.jiskha.com/display.cgi?id=1291874924

Answer 2

let e^x = t
then
e^2x – 12e^x =13 becomes
t^2 - 12t - 13 = 0
(t-13)(t+1) = 0
t = 13 or t = -1

then e^x = 13 or e^x = -1
x = ln 13 or x = ln(-1)
but in ln(a) a > 0

so x = ln 13

Answer 3

I slipped in the sign of the transformed equation. Instead of
y²-12x+13=0
it should read
y²-12x-13=0

Go with Reiny's solution.

Answer 4

Thank u both