SOLUTION: Solve the exponential equation. Use a calculator to obtain a decimal approximation,correct to two decimal places, for the solution. e^2x + e^x -6=0

Question 245546: Solve the exponential equation. Use a calculator to obtain a decimal approximation,correct to two decimal places, for the solution.
e^2x + e^x -6=0

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
e^2x + e^x -6=0
.
Let A = e^x
then we can rewrite:
e^2x + e^x -6=0
as
A^2 + A -6=0
Factoring
(A+3)(A-2) = 0
A = {-3, 2}
.
But, we said:
A = e^x
Solving for x:
ln(A) = x
.
At this point, we can toss out the negative solution leaving:
A = 2
ln(A) = x
ln(2) = x
0.69 = x

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