It gives infinity. ln∞ does tend to infinity, but not very fast.
Keep in mind though, that infinity isn't like any ordinary number. ∞+∞ = ∞, for example.
doesn't give anything. "Infinity" is not a real number and ordinary functions such as "logarithm" and "subtraction" do not apply to it. There are extended number systems in which "infinity" is defined as a number but they still do not apply "logarithm" or "subtraction" in the usual sense.
Something of the form lim [f(x)- ln(g(x))] where and may exist but the limit will depend upon exactly how f and g "go to infinity".
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