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

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- Mar 19th 2008, 11:13 AMangelus2402004Help 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 - Mar 19th 2008, 11:45 AMwingless
Let $\displaystyle a = e^x$.

Then $\displaystyle a^2 = e^{2x}$

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

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

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

Then use $\displaystyle x = \ln a$..... - Mar 19th 2008, 12:35 PMangelus2402004
Thank You!