perplexus.info :: Just Math : Fortieth logs

Fortieth logs (Posted on 2011-05-31)

It turns out that the common logarithms of each of the numbers from 2 through 9 can be very well approximated by rational numbers of the form n/40.

Derive each of the numerators with no calculation aids beyond pencil and paper.

See The Solution Submitted by Jer

Rating: 4.5000 (2 votes)

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Lucky 7

| Comment 5 of 15 |

Well, now that we know log 5,

7^2 = 49 ~ 50

so 2log 7 ~ log 50 = 1 + log 5 ~ 1+ 28/40 = 68/40

==> log 7 ~ 34/40

Posted by Steve Herman on 2011-05-31 21:13:59

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