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Strange behavior of Simplify


I've just run across the following strange behavior of Simplify.
(Using Mathematica 4.1.5, Mac OS X).

These first two commands work as expected:

        Simplify[Exp[2*n*(Log[1 + t] - Log[1 - t])]]

                       (1 - t)^(-2*n) (1 + t)^(2*n)

        Simplify[Exp[n^2*(Log[1 + t] - Log[1 - t])]]

                       (1 - t)^(-n^2) (1 + t)^(n^2)

But Simplify refuses to do anything with this:

        Simplify[Exp[2*n^2*(Log[1 + t] - Log[1 - t])]]

                      Exp[2*n^2*(Log[1 + t] - Log[1 - t])]

Can anyone shed some light here?  By the way, FullSimplify does the 
same thing.


-----
Selwyn Hollis
http://www.math.armstrong.edu/faculty/hollis



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