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 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

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

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

Jan 7, 2016 · dy/dx=1 y=e^(lnx)=x. (By properties of logs). therefore dy/dx=d/dx x = 1. Alternatively, we may apply the derivative of the whole function before simplifying it and will get the same final answer :\\ d/dx e^(lnx)=e^(lnx)*1/x =x*1/x =1.

Feb 10, 2016 · Given fuction is e^(3lnx) Now, we know the logarithmic identity logm^n=nlogm and m^(log_mn)=n So using the above identities, we can reduce the equation. e^(3lnx)=e^ln(x^3)=x^3 So there you have it.

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

Feb 25, 2016 · e^(3lnx)= x^3 Let e^(3lnx)=k, then lnk=3lnx. But 3lnx=ln(x^3), therefore lnk=ln(x^3), i.e. k=x^3 Hence, e^(3lnx)=x^3

The composition of all inverses results in the identity function: f(x) = x. Using Algebra: Find the natural logarithm of each side: Use the property of logarithms, to move the exponent of the argument in front of the logarithm: By definition, ln(e) = 1: By the Identity Property of Multiplication the left side simplifies to: