I want to be able to expand $\log(x^n e^x) = n \log(x) +x$:
FullSimplify[Log[x^n Exp[x]], x > 0 && Element[n, Integers] && n > 1]
-1 +FullSimplify[Log[x^n Exp[x]] + 1, x > 0 && Element[n, Integers] && n > 1]
x + n Log[x]
what gives? Maybe it recognizes that I want to do arithmetic outside the log, so it then simplifies the expression; if that's the case, how can I force it to do that without hacking it by adding and subtracting 1?