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How to treat this false singular point?


Dear everyone,
I have a function:
f[x_]:=(x-x1)Log[Abs[x-x1]] + (x-x2)Log[Abs[x-x2]] + ... +
(x-xn)Log[Abs[x-xn]],
{x1,x2,...,xn}={100,200,300,...} for instance
How to get value: f[x] as there are different singular at different x?
I know at x=xn, f[x]==1, But Mathematica return: "Indeterminate", What
should I do?
 what others do in C++, Fortran ?


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