To plot the function f(x, y) = ln(x^2 + y^2) in Mathematica, users can utilize the Plot3D command with the syntax Plot3D[Log[x^2 + y^2], {x, xmin, xmax}, {y, ymin, ymax}]. For symmetry in both x and y axes, it is recommended to set xmin equal to ymin and xmax equal to ymax. Additionally, users can define the function as f[x_, y_] = Log[x^2 + y^2] and then plot it using Plot3D[f[x, y], {x, xmin, xmax}, {y, ymin, ymax}]. To achieve a cylindrical coordinate representation, the ParametricPlot3D command can be used. Properly configuring these commands allows for accurate three-dimensional visualizations of the function.