Plotting f (x, y) = ln(x^2 + y^2 ) - Mathematica Help

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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.
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I'm trying to plot this
f (x, y) = ln(x^2 + y^2 )

any one got a idea how to?
 
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Plot3D[f, {x, xmin, xmax}, {y, ymin, ymax}]
make a three-dimensional plot of f as a function of the
variables x and y
 
More accurately,

Plot3D[Log[x^2 + y^2], {x, xmin, xmax}, {y, ymin, ymax}]

or

f[x_,y_]=Log[x^2 + y^2]
Plot3D[f[x,y], {x, xmin, xmax}, {y, ymin, ymax}]
 
i want to make this symmetric in both x and y with 2 graph by using the cartesian coordinate system with the plot3D command and secondly using the cyclindrical coordinate system using the parametricplot3d command. been a long time since I've used mathematica but i don't think your codes does the above right?
 
anyone ?
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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