e^2x =3e^-1/4x

e^2x =3e^-1/4x

So what would happen if i divided by e^-1/4x....

I would have e^2x / e^-1/4x = 3

The answer is x=4/9In3 but im not too sure how to get that far......

Reply 1

k@tie

10

e^2x =3e^-1/4x
e^(2x) = e^(ln3 - 1/4x)
2x = ln3 - 1/4 x
(9/4) x = ln3
x=(4/9)ln3

Reply 2

Newton

(e^(2x))=3(e^(-x/4))

If you were do divide through by (e^(-x/4)), according to the laws of indices ((e^ax)/(e^bx))=(e^(a-b)x),

((e^2x)/(e^(-x/4))=3

=>(e^(2--(1/4))x)=(e^(2+(1/4))x)=(e^(9/4)x)

=>(e^(9/4)x)=3

=>(9/4)x=log3

=>x=(4/9)log3 Q. E. D.

You could also have taken the logarithm of both sides at the beginning,

2x=log3-(1/4)x

=>2x+(1/4)x=log3

=>(9/4)x=log3

=>x=(4/9)log3 Q. E. D.

Newton.