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# e4x-13e2x+12=0

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e4x-13e2x+12=0

Guest Mar 4, 2015

#1
+27219
+10

$$e^{4x}-13e^{2x}+12=0$$

This can be written as:

$$(e^{2x})^2-13e^{2x}+12=0$$

which can be written in turn as:

$$(e^{2x}-1)(e^{2x}-12)=0$$

So we have:

1.

$$\\e^{2x}=1\\so\\x=0$$

2.

$$\\e^{2x}=12\\\\2x=\ln{12}\\\\x=\frac{\ln{12}}{2}$$

.

Alan  Mar 4, 2015
#1
+27219
+10

$$e^{4x}-13e^{2x}+12=0$$

This can be written as:

$$(e^{2x})^2-13e^{2x}+12=0$$

which can be written in turn as:

$$(e^{2x}-1)(e^{2x}-12)=0$$

So we have:

1.

$$\\e^{2x}=1\\so\\x=0$$

2.

$$\\e^{2x}=12\\\\2x=\ln{12}\\\\x=\frac{\ln{12}}{2}$$

.

Alan  Mar 4, 2015