Jan 23, 2014 · I have a hard time understanding why $\\ln e=1$ Can someone explain to me why the natural logarithm of e is exactly equal to the first nonzero but positive integer?

Oct 7, 2017 · ln(lne) = ln1 = 0 The logarithm on base a of a is always 1, since a1. In addition, it has to be a> 0 and a other than 1, so that there are no problems.

Mar 14, 2020 · I don't really understand the step by step procedure on how to calculate this? That $-$ confuses me, because I don't understand how there can be an $\\ln$ of a negative number. Can …

Apr 11, 2014 · $\frac d {dx} (ln x)=\lim_ {u \to +\infty} (\frac ux (ln (1+\frac 1u)))$ = $\lim_ {u \to +\infty} (\frac 1x (ln (1+\frac 1u)^ {u})$ = $\frac 1x lne$. Now integrate both sides to get the result.

I am nit sure it is a proof....but anyway: From the definition of log: log_bx=a auch that: x=b^a that is, the integrand is equal to the base to the power of the result. In our case we know that the Natural …

Apr 12, 2018 · I was trying to do an integration problem with u sub and got stuck, one part of the equation was this $\\ln(e^{2x+1})$ this is suppose to simplify really nicely according to a site, is there …

Taking logs of both sides, # lne^x=ln [1/sqrt [e-1]]# #but ln [e^x]=x# and so #x=ln [1/sqrt [e-1]]#. Hope this helps. Answer link

Oct 31, 2021 · The natural logarithm is multivalued with respect to complex numbers. This means that the natural logarithm is not a function because its outputs are not unique. In order to deal with this, …

Do you know the formula for finding the foot of the perpendicular from a given point to a given line?

Dec 5, 2023 · Expanding on Henning's comment, even "ln" is ambiguous in the wider community because it's interpreted as short for "logarithm" versus the esoteric "logarithmus naturalis" (in which …