Question 220511: Can someone help me with this problem?
If e^{2x} + 4e^{x} = +12, then x = Found 2 solutions by stanbon, Alan3354:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Can someone help me with this problem?
If e^{2x} + 4e^{x} = +12, then x =
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That is a quadratic function with variable = e^x
Let e^x = w
Rewrite the equation and solve for "w":
w^2 + 4w - 12 = 0
Factor:
(w+6)(w-2) = 0
w = -6 or w = 2
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Substitute back to e^x
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e^x = -6 or e^x = 2
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Solve for "x":
e^x cannot be negative so it cannot be -6.
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e^x = 2
x = ln2 is the only solution.
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Cheers,
stan H.
You can put this solution on YOUR website! e^{2x} + 4e^{x} = +12
e^{2x} + 4e^{x} - 12 = 0
It's a quadratic in e^x
(e^x + 6)*(e^x - 2) = 0
e^x = -6 --> x = ln(-6) NG, ignore
e^x = 2 --> x = ln(2)
x =~ 0.69314
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