Question

e^2x=e^x^2-8

Answer 1

Hey Marie :)\[\Large\rm e^{\color{orangered}{2x}}=e^{\color{orangered}{x^2-8}}\]Notice, that since our bases are the same,

Answer 2

our exponents will be the same also,\[\Large\rm \color{orangered}{2x=x^2-8}\]

Answer 3

So you have a quadratic in x.
Do you know how to solve it from there? :)

Answer 4

@mariela98

Answer 5

\[e^{2x} = e^{x^2 -8}\]Raise both sides by \(\log_e\)\[\log_e (e^{2x})=\log_e (e^{x^2-8})\]\[2x = x^2 - 8\]solve the quadratic :) \[x^2-2x-8=0\]

Answer 6

thank you both :)

Answer 7

did you find an answer? :o