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| ``Re: Logarithms: Something more is needed''
by knodeltheory on 2008-06-13 12:05:15 |
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| Put even more simply: you use the table of logaritmhs to step down the inputs and you use the same table to step up the output.
Provided of course that the table goes far enough in the necessary direction. Here's an example contrived not to be out of range for this table: multiply 12 by 8. Log 12 is 2.48491, according to the table, and log 8 is 2.07944. Add those logs up you get 4.56435. You look 4.56435 up in the table and find it at the position corresponding to 96. Obviously it would've been easier to just mentally calculate 8 * 10 + 8 * 2, which is why Babbage's table went up to 108,000. However, I think Babbage's table only had four decimal places for each entry, so in that sense this table is "wider" than Babbage's.
There is something almost miraculous about actual numbers. A scary concept like negative infinity (for log 0) doesn't seem as foreboding put in the company of numbers like 2.3 and 0.6. |
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