How to find the time with rate proportional equation

The video tutorial explains how to determine the time it takes for the amount of oil pumped under a well to decrease to one-fifth of its current value, given a continuous decrease rate of 10% per year. The instructor discusses the initial and final values, the rate of decrease, and how to solve for time using logarithms. Various methods to express the solution are explored, emphasizing understanding different approaches to the problem.

What is the mathematical expression used to find T in the context of the oil pumping problem?

Can you explain the different ways to express the logarithmic equation derived from the oil pumping scenario?