Show that the applications
$$h_1 : \left|\begin{array}{rll} \mathbb{R}^2 \backslash \{(0,0)\} & \rightarrow & \mathbb{R} \\ (x,y) & \mapsto & \ln(x^2 + y^2) \end{array}\right. \quad \text{and} \quad h_2 : \left|\begin{array}{rll} \mathbb{R}^2 \backslash \{(0,0)\} & \rightarrow & \mathbb{R} \\ (x,y) & \mapsto & \dfrac{1}{x^2 + y^2} \end{array}\right.$$
are harmonic.