![derivative of log base a derivative of log base a](https://themathpage.com/aCalc/calc_IMG/0152.gif)
How, I wondered, were fractional and irrational powers calculated? It is, of course, easy to calculate integer powers such as 10 2 and 10 3, and in a pinch you could even calculate 10 2.5 by finding the square root of 10 5.
![derivative of log base a derivative of log base a](https://showme0-9071.kxcdn.com/files/1000120823/pictures/thumbs/2570156/last_thumb1484596224.jpg)
We were studying common logarithms in school, and I marveled at their ability to turn complicated multiplication problems into simple addition just by representing all numbers as fractional powers of 10. I still remember my first introduction to e. Like its transcendental cousin π, e can be represented in countless ways - as the sum of infinite series, an infinite product, a limit of infinite sequences, an amazingly regular continued fraction, and so on. But why, in our puzzles, does it seemingly appear out of nowhere?īefore we attempt to answer this question, we need to learn a little more about e’s properties and aliases. Most familiar as the base of natural logarithms, Euler’s number e is a universal constant with an infinite decimal expansion that begins with 2.7 1828 1828 45 90 45… (spaces added to highlight the quasi-pattern in the first 15 digits after the decimal point). Hidden below the surface was the mysterious transcendental number e. Last month, we presented three puzzles that seemed ordinary enough but contained a numerical twist.