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Ok OP, to explain this you're gonna need a little bit of context on e and what it does.
The number e is essential in problems of exponential growth. Sure, e can be defined with different sums, like 1/0! + 1/1! + 1/2! + 1/3! + 1/4!..., but if you want to hear about the growth part, let's start with an experiment. Say I find a bank with 100% interest, and I start by putting $1 in. After a year, I'll have $2. Let's just say that another bank has 50% interest every 6 months. After a year, I'll have $2.25. If another bank split's it into 33% interest every 4 months, I'll have $2.37. If we continue along down this line, this sequence will eventually converge to e. The thing is, you can get a formula for any nth term in this sequence. It's (1 + 1/n)^n. E is used to calculate exponential growth when taken to the power of a number. So therefore, reversing this power (taking the logarithm) lets us figure out what we need to grow TO a number.
