Question

(2x) ^ln2 = (3y)^ln3
Solve for x

Answer 1

Given,

(2x)^ln2= (3y)^ln3

taking log both sides we get

ln2.log(2x)= ln3.log(3y)

Now differentiate w.r.t. x we get

ln2.(1/2x).d/dx(2x)= ln3.(1/3y).d/dx(3y)

=> ln2/2x.(2)=ln3/3y.(3dy/dx)

=> ln2/x= ln3/y.dy/dx

=>dy/dx=(ln2/ln3).(y/x) Ans.