It's based on the idea of "how long would it take me to double my money with this much compound interest?", although for that question, it looks more like log(2)/log(1.04). I'm not sure what it's called, but a maths teacher showed it to me once, and it's been retained in memory.
The unscientific alternative (but a great way to make sure that your numbers are somewhat accurate) is to repeatedly multiply the number in the second log term by itself repeatedly, until the result passes the first number. I tried this first, but lost count, and then I remembered the log/log trick.
It works with whichever base your logarithms are in (10, e, 2 being the standard ones), just as long as you use the same type for both terms.
The unscientific alternative (but a great way to make sure that your numbers are somewhat accurate) is to repeatedly multiply the number in the second log term by itself repeatedly, until the result passes the first number. I tried this first, but lost count, and then I remembered the log/log trick.
It works with whichever base your logarithms are in (10, e, 2 being the standard ones), just as long as you use the same type for both terms.
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