I haven’t had calc for like… 2 semesters, and a friend asked me to check over his work to see if he had made some eggregious error. I searched Google real quick, and my log rules are fuzzy, at best.

Is there a way to simplify ln(e^(x) + 1) any further? I’m leaning heavily towards no.

I don’t think that there’s any way ln(e[sup]x[/sup]+1) can be simplified.

Near x=0, I suppose you could expand e[sup]x[/sup], in terms of a series expansion, and then discard higher order terms, and then expand the resulting log, again in terms of a power series.

But I can’t see any reason why one would want to do that. Why do you want to simplify it?