perplexus.info :: Algorithms : Just by hand, only by hand, nothing but by hand?

Just by hand, only by hand, nothing but by hand? (Posted on 2004-07-26)

Imagine you are living a lot of years ago, without calculators, slide rules, tables of logarithms, or any kind of tool but paper and pencil... how would you go about calculating log₁₀ of 2 -- or of any other number?

By the way, if your solution required calculating powers, or if you just wanted to check your solution, how would you calculate 10 to the 0.30103... power, or any other?

Submitted by Federico Kereki

Rating: 4.1667 (6 votes)

Solution: (Hide)

The key is using binary numbers, and the fact that we can calculate square roots.
Calculate N1=√10, N2=√√10, N3=√√√10, ... and so on. If, for example, the number whose logarithm we are looking for was approximately N1xN3xN4, then its logarithm would be 1/2^1+1/2^3+1/2^4.
For the second problem, first write N as the sum of binary powers (say, N=1/2^1+1/2^3+1/2^4+...) and to calculate 10^N, multiply the appropriate roots of 10, as in the first part.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
solng	neshal	2004-08-02 07:19:58
No Subject	jason	2004-07-31 22:32:08
Re: Im really cant remember	jason	2004-07-31 22:25:36
re: put another way	Richard	2004-07-26 23:30:13
One Solution (first part)	DJ	2004-07-26 14:34:32
put another way	Charlie	2004-07-26 14:13:44
A Very Primitive Method	Richard	2004-07-26 13:49:47

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