SOLUTION: Can someone help me with this problem? If e^{2x} + 4e^{x} = +12, then x =

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
---------------------
Substitute back to e^x
---
e^x = -6 or e^x = 2
-----------------------
Solve for "x":
e^x cannot be negative so it cannot be -6.
-------------
e^x = 2
x = ln2 is the only solution.
===================================
Cheers,
stan H.
Answer by Alan3354(69443) (Show Source): 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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