Intuition behind natural log and e
The following are a set of nice explainers about intuition for what e and ln mean, and why we use them constantly to discuss growth rates. You can surf through them to refresh your use of them, but I’ll highlight something the sites bring up a lot.
e tells you how much growth has occurred after a given amount of time. So egt tells you by how much something is scaled up after growing at a rate g for t periods.
ln tells you what it takes to reach a given amount of growth. So ln(x) will tell you the combination of growth rate g and time t that it takes to scale something up by a factor of x.
I think this post is the best one overall: How To Think With Exponents And Logarithms
The rest of these are also useful:
An Intuitive Guide To Exponential Functions & e
Demystifying the Natural Logarithm (ln)