I know that ln(x) is defined as the integral of 1/t from 1 to x. What is the logical connection between that integral and ln(x)? Why is it that way?
This is a discussion on ln calculus within the A Brief History of Cprogramming.com forums, part of the Community Boards category; I know that ln(x) is defined as the integral of 1/t from 1 to x. What is the logical connection ...
I know that ln(x) is defined as the integral of 1/t from 1 to x. What is the logical connection between that integral and ln(x)? Why is it that way?
AFAIK, ln x is defined as the following:
e^y=x ---> ln(x)=y
Although what you are saying is true, I have never heard of it being used as the definition of ln.
I'll rephrase...
why is the integral of 1/t from 1 to x, ln(x)? What connection is there between a log and an integral? (ie: why does this connection exist?)