# Thread: Help with solving exponential equation

1. ## Help with solving exponential equation

I can't figure out how to factor out this quadratic exponential equation

e^2x+7e^x-3=0

The answer in the book says it is -0.904 but I don't know how to figure out how to get the answer.

Thank you

2. Let $a = e^x$.
Then $a^2 = e^{2x}$

$e^{2x} + 7 e^x - 3 = 0$

$a^2 + 7a - 3 = 0$

$a = \frac{-7\pm \sqrt{49 + 4.3}}{2}$

Then use $x = \ln a$.....

3. Thank You!