Question

let (x',y') be the solution of the following equation:
(2x)^ln2=(3y)^ln3
3^lnx=2^lny.
then x' is ?

Answer 1

2x^ln2 = 3y^ln3
which means that 3y = (2x)^(ln2-ln3)
which means that 3y = (2x)^(ln(2/3))
or y = (2x)^(ln(2/3))
substitute in the other equation and solve for x

Answer 2

sorry, y = ((2x)^ln(2/3))/3

Answer 3

i disagree, 2x^(ln2/ln3) does not equal 2x^(ln2-ln3)
->y = ((2x)^(ln2/ln3))/3

Answer 4

i get x' = 1/2, y' = 1/3

Answer 5

oh, dumbcow is right, I made a mistake there