# Help with solving exponential equation

• March 19th 2008, 11:13 AM
angelus2402004
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
• March 19th 2008, 11:45 AM
wingless
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 $x = \ln a$.....
• March 19th 2008, 12:35 PM
angelus2402004
Thank You!