e4x-13e2x+12=0

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

 

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.

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

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