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Just P&P (Posted on 2011-01-23) Difficulty: 3 of 5
No calculator, no tables-
Please evaluate lg 7 within .01.

Rem: lg 7 is a decimal (by base 10) logarithm of 7.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

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Some Thoughts just a digression (though spoiler is present) | Comment 1 of 6

This is just a digression, as it incorporates a table, albeit one that is in my head.

Years ago, sitting in a coffee shop across Broadway from one of the entrance portals to the Columbia University campus, I noticed an address marker for that entrance on Broadway that had a graffito enhancement stenciled on it. The address, 3010, had been prefaced with "log 2 = .", and so the log of 2 stuck in my mind as .3010.

Familiarity with slide rules impressed on my mind that log(3) was just under .5, and it didn't take much memorization to remember it as .48.

Log(4) and log(8) are of course twice and three times log(2), and log(5) is just 1 - log(2), and log(9) is of course twice log(3).

That leaves us just to interpolate between log(6) = log(2) + log(3) = .78 and log(8) = .90. Examination of all the values indicates that linear interpolation is probably sufficient, leading to log(7) ~= .84, which is within .01 of the more accurate .845098, although not properly rounded.

  Posted by Charlie on 2011-01-23 12:33:48
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