(In reply to re: almost proof NOT TRUE
by Ady TZIDON)
No, Dixi, Daniel is right. Dividing one integer by another always yields a rational number. The result can never be irrational. There are no integers p,q such that p/q=ln(3)/ln(2).
Your "counterexample" shows that dividing one irrational by another can yield a rational number, but that does not refute Daniel's logic.