Nov 11, 2015 · It is exactly x. You are looking for a number that is the exponent of the base of ln which gives us the integrand, e^x; so: the base of ln is e; the number you need to be the exponent of this base to get e^x is.....exactly x!!! so: ln(e^x)=log_e(e^x)=x

Mar 28, 2018 · x ln(e^x)=x because log_a(a^x) is x. 106147 views around the world You can reuse this answer

Oct 23, 2015 · It's x. The logarithm and the exponential are inverse function, which means that if you combine them, you obtain the identity function, i.e. the function I such that I(x)=x. In terms of definitions, it becomes obvious. The logarithm ln(x) is a function which tells you what exponent you must give to e to obtain x. So, e^(log(x)), literally means: "e to a power such that e to that …

Jun 8, 2015 · It is because log of x to the base e is ln x, that is # log_e x = ln x#. This means #e^lnx = x# Answer link.

Mar 22, 2016 · e^lnx=x let y=e^lnx ln y=lne^lnx->Take ln of both sides lny = lnx * ln e -> use the property log_b x^n = nlog_b x lny=lnx(1)-> ln_e e = 1-> from the property log_b b = 1 lny = ln x Therefore y=x

Aug 25, 2016 · ln e^(2x) = 2x As a Real valued function, x |-> e^x is one to one from (-oo, oo) onto (0, oo). As a result, for any y in (0, oo) there is a unique Real value ln y such that e^(ln y) = y. This is the definition of the Real natural logarithm. If t in (-oo, oo) then y = e^t in (0, oo) and from the above definition: e^(ln(e^t)) = e^t Since x |-> e^x is one to one, we can deduce that for any …

Aug 23, 2017 · The range of e^x is CC "\" { 0 }. e^x is continuous on the whole of CC and infinitely differentiable, with d/(dx) e^x = e^x. e^x is many to one, so has no inverse function. The definition of ln x can be extended to a function from CC "\" { 0 } into CC, typically onto { …

Mar 31, 2016 · Use some logarithm properties and the fact that d/dx(lnx)=1/x to get dy/dx=-x/(1+x). Begin by factoring out an e^-x within the parenthesis: y=ln(e^-x(1+x)) Now apply the property ln(ab)=ln(a)+ln(b) to get: y=ln(e^-x)+ln(1+x) Apply another property specific to the natural logarithm, ln(e^a)=a: y=-x+ln(1+x) We can now take the derivative with ease. Using the sum …

Feb 6, 2016 · #color(brown)("Total rewrite as changed my mind about pressentation.")# #color(blue)("Preamble:")# Consider the generic case of #" "log_10(a)=b#

Mar 3, 2016 · e*x Use the rule to split up the exponent: a^(b+c)=a^b(a^c) Thus: e^(1+lnx)=e^1(e^lnx) Here: e^1=e e^lnx=x So: e^(1+lnx)=e*x