Simplifying Ln(e^(x) + 1) - Straight Dope Message Board Home » Approximation Ln(1+exp(x)) » Simplifying Ln(e^(x) + 1) - Straight Dope Message Board Maybe your like Approximation Logarithmic Integral Approximation Logarithmus Approximation Of Average Sea Level Atmospheric Pressure Approximation Of Pi Is Approximation Of Pi Javascript Simplifying ln(e^(x) + 1) Factual Questions Civil_Defense January 21, 2004, 6:45pm 1 Bah. 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. Achernar January 21, 2004, 6:50pm 2 Civil Defense: Is there a way to simplify ln(e^(x) + 1) any further? I’m leaning heavily towards no. No. I was going to say you could make an approximation near x=0 that’s simpler, but I don’t even think that’s the case. Jabba January 21, 2004, 6:51pm 3 No, there isn’t. You can write it in a couple of other equivalent forms, but I wouldn’t call them simpler. Angua January 21, 2004, 9:18pm 4 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? ultrafilter January 21, 2004, 9:46pm 5 The most you can say is that ln(e[sup]x[/sup] + 1) is approximately equal to x, with the approximation being better for larger values of x. Achernar January 21, 2004, 9:56pm 6 Actually, at the other end of things, ln(exp(x) + 1) = exp(x) is good to better than 1% for x < -4. Thudlow_Boink January 21, 2004, 11:39pm 7 Did you double check to make sure it wasn’t really supposed to be ln(e^(x+1))? That, of course, you could simplify. Achernar January 21, 2004, 11:48pm 8 And! The graph of this function can be expressed parametrically as: x = 2ln(sinh(t)) y = 2ln(cosh(t)) That’s pretty simple, huh? Related topics Topic Replies Views Activity Math Help - logarithms Factual Questions 24 1316 October 17, 2001 Show ln x/x < 1/e without derivatives? Factual Questions 23 6702 May 12, 2006 What exactly do e, Log and ln mean in math Factual Questions 21 16287 September 14, 2004 Please check this method of finding the derivative of ln(x) Factual Questions 11 877 February 7, 2018 Derivative of the natural log Factual Questions 12 2265 February 28, 2012 Tag » Approximation Ln(1+exp(x)) Approximating $\ln(1+\exp(x)+\exp(y))$ - Mathematics Stack Exchange Is Ln(1+exp(x)) = X When X Is A Large Number? - Physics Forums Linearized Approximation Of The Ln (1 − Exp (−x)) Term. Linearized Approximation Of The Ln (1-exp(-x)) Term - ResearchGate [PDF] NEW CLOSE FORM APPROXIMATIONS OF Ln(1 + X) Maclaurin Series Of Ln(1+e^x) - YouTube Maclaurin Series Of Ln(1+e^x) - YouTube Can The Given [math]\ln (1-e^{-x})[/math] Be Written In A Series With ... Taylor Series - Wikipedia [PDF] Accurately Computing Log(1 - Exp(.)) – Assessed By Rmpfr [PDF] Taylor Series
