Question

I need to show that the ln of the absolute value of x (a 2-d vector) is a harmonic function which means that the laplace operator of that function gives 0 for all x. Somehow it does not work. What am I doing wrong? You can see my calculation on the picture.

Answer 1

I looked at your work and my suggestion would be to switch to polar coordinates and run the algebra one more time. It'll be easy to work with then