3 ms·
> 3^2.5, what does it mean to say "multiply 3 by itself 2.5 times?" It means 3 · 3 · √3. If you write the exponent in binary, you can approximate any such powe
by jacobolus 3y ago
> 3^2.5, what does it mean to say "multiply 3 by itself 2.5 times?"
It means 3 · 3 · √3. If you write the exponent in binary, you can approximate any such power as a product of various repeated square roots.
> how the heck they worked out these log values in the beginning
If you're really curious about the very beginning, here's an English translation of Briggs's (1624) book: https://17centurymaths.com/contents/albriggs.html https://17centurymaths.com/contents/albriggs.html
And here are English translation of Napier's (1614, 1619) books: https://17centurymaths.com/contents/napiercontents.html https://17centurymaths.com/contents/napiercontents.html
- svat 3y agoA few years ago, I wrote a summary of Napier's conception and construction here: https://math.stackexchange.com/questions/47927/motivation-for-napiers-logarithms/48036#48036 https://math.stackexchange.com/questions/47927/motivation-fo...
- lifthrasiir 3y agoWikipedia has a concise enough explanation of Napier's invention and its peculiarity compared to the modern definition [1]. [1] https://en.wikipedia.org/wiki/History_of_logarithms#Napier https://en.wikipedia.org/wiki/History_of_logarithms#Napier
- mindcrime 3y agoOf course Wikipedia has a page titled "History of logarithms"! I should have just looked there first. :-)
- jacobolus 3y agoA better source is Cajori's (1913) 7-part history of logarithms in the American Math Monthly, [20(1) 5–14](https://www.jstor.org/stable/2973509 https://www.jstor.org/stable/2973509), [20(2) 35–47](https://www.jstor.org/stable/2974078 https://www.jstor.org/stable/2974078), [20(3) 75–84](https://www.jstor.org/stable/2973441 https://www.jstor.org/stable/2973441), [20(4) 107–117](https://www.jstor.org/stable/2972960 https://www.jstor.org/stable/2972960), [20(5) 148–151](https://www.jstor.org/stable/2972412 https://www.jstor.org/stable/2972412), [20(6) 173–182](https://www.jstor.org/stable/2973069 https://www.jstor.org/stable/2973069), [20(7) 205–210](https://www.jstor.org/stable/2974104 https://www.jstor.org/stable/2974104)