You can put this solution on YOUR website! 6e^(2x)-16e^x=6
3e^2x - 8e^x - 3 = 0
It's a quadratic in e^x. You can sub y for e^x if it makes it clearer.
--> y^2 - 8y - 3 = 0
I'll just do it with e^x
(3e^x + 1)*(e^x - 3) = 0
e^x = 3
x = ln(3)
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e^x = -1/3 Ignore this one, no exponent will give a negative (in real numbers)
You can put this solution on YOUR website! 6e^(2x)-16e^x=6
solve for x. please explain
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This is a quadratic equation with e^x as it's variable:
Rewrite:
6(e^x)^2 - 16(e^x) - 6 = 0
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Let m = e^x
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6m^2 - 16m - 6 = 0
3m^2 - 8m - 3 = 0
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3m^2 -9m+m - 3 = 0
3m(m-3)+(m-3) = 0
(m-3)(3m+1) = 0
m = 3 or m = -1/3
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Substitute to solve for "x":
e^x = 3
x = ln(3) = 1.098612...
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e^x = (-1/3)
No solution because no value of e is negative.
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Cheers,
Stan H.
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