Re: Log (base 2) of 3 -- (without a Calculator)

On Tue, 19 Nov 2024 19:47:00 +0000 (UTC), Richard Tobin wrote:

In article <97e7e6fb078310c8d4d600c247847957@www.novabbs.com>,
HenHanna  <HenHanna@dev.null> wrote:
 

i wonder if there's a way to get better (and better) approximations.

 
Look for more powers of 2 near to powers of 3.
 
For example,
 
3^7  (= 2187)  > 2^11 (= 2048),  so 3 > 2^(11/7),  so log2(3) > 11/7 =
1.571+
3^10 (= 59049) < 2^16 (= 65536), so 3 < 2^(16/10), so log2(3) < 10/6 =
1.6
 
3^12 is very close to 2^19, so log2(3) is very close to 19/12 = 1.583+
 
-- Richard

That's a very nice explanation.

Not a direct answer to HenHanna's original question, but interesting none
the less. I was trying to work out how Babbage's difference engine, using
finite differences, could be used to perform relaterd calculations.I got a
bit distracted, but the following translation of Briggs' ARITHMETICA
LOGARITHMICA was very informative.

https://www.17centurymaths.com/contents/albriggs.html



--
David Entwistle