Question

Find all real number solutions to the system of equations:
y=e^(4x)
y=e^(2x)+6

Answer 1

\[e^{4x}=e^{2x}+6\]\[e^{4x}-e^{2x}-6=0\]\[(e^{2x}+2)(e^{2x}-3)=0\]\[e^{2x}=3\quad\Rightarrow\quad y=9\]\[x=\ln{\sqrt{3}}\]

Answer 2

e^4x = e ^ 2x + 6
e^4x - 6 ^2x - 6 = 0
( e^2x + 2) (e^2x - 3) = 0
e^2x = 3 > y = 9



x = In √3