Cinsider three utility functions u, v, w defined on strictly positive vectors with x₁, x₂ > 0. Show that u and v are equivalent to one another, but that they are not equivalent to w.

1) u(x₁, x₂) = ln x₁ +ln x₂

2) v( x₁, x₂) = x₁x₂

3) w( x_1, x2) = 2x_{1 +} 3x₂