Verify that the function u (x, y) = ln (x 2 + y 2 ) + b satisfies Laplaces equation (3) and determine

Verify that the function u (x, y) = α ln (x² + y²) + b satisfies Laplace’s equation (3) and determine α and b so that u satisfies the boundary conditions u = 110 on the circle x² + y² = 1 and u = 0 on the circle x² + y² = 100.