# Thread: an a level exponential

1. ## an a level exponential

Hello, i have just finished one of my A level papers, i think i aced it except for the first question, and any fluffy mistakes i made.

e^x +3e^-x = 4

solve it!

after the customery after test discussion there seemed to be a differant answer for each student, and in one special case 4.

Can anybody please solve this question for me, as its bugging me pretty badly.

Thank you

2. Originally Posted by pablohacker
Hello, i have just finished one of my A level papers, i think i aced it except for the first question, and any fluffy mistakes i made.

e^x +3e^-x = 4

solve it!

after the customery after test discussion there seemed to be a differant answer for each student, and in one special case 4.

Can anybody please solve this question for me, as its bugging me pretty badly.

Thank you
$\displaystyle e^x +3e^{-x} = 4$<-- Multiply both sides by $\displaystyle e^x$

$\displaystyle e^{2x} + 3 = 4e^x$

$\displaystyle e^{2x} - 4e^x + 3 = 0$

Let $\displaystyle y = e^x$

Then
$\displaystyle y^2 - 4y + 3 = 0$

$\displaystyle (y - 1)(y - 3) = 0$

Thus
$\displaystyle y = 1$ ==> $\displaystyle e^x = 1$ or $\displaystyle x = 0$
or
$\displaystyle y = 3$ ==> $\displaystyle e^x = 3$ or $\displaystyle x = ln(3)$

-Dan