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 2005-07-16, 15:46 #1 Numbers     Jun 2005 Near Beetlegeuse 22·97 Posts Converting Logs I was actually rather interested in the math content of an earlier thread, so if no one minds I would like to re-visit that topic. The discussion was about converting logs from one base to another, and especially to base e. I wasnâ€™t able to follow the example given, but have come up with the following: If y = a^x, then log(y) = xlog(a) So log(y) / log(a) = x So to convert from log_10 to log_e I get Log_10(y) / Log_10(e) = base e log of y Is this correct?
 2005-07-16, 17:03 #2 Mystwalker     Jul 2004 Potsdam, Germany 3·277 Posts If I haven't misread something, that is totally correct (and the way to use when a calculator only has log_10).
 2005-07-16, 18:32 #3 Numbers     Jun 2005 Near Beetlegeuse 22×97 Posts Thank you very much. Maybe I was able to follow the other example after all.
 2005-07-16, 23:21 #4 dsouza123     Sep 2002 2×331 Posts And e (in base 10) is 2.718281828 to 9 places after the decimal point. To get e take the inverse natural log of 1, using the Windows XP calculator in Scientific mode press 1 Inv ln
 2005-07-17, 00:17 #5 Numbers     Jun 2005 Near Beetlegeuse 22×97 Posts e by gum dsouza123, That would account for my error. I had been using the series 1 + 1/1! + 1/2! + ... 1/12! which gives 2.7182818283, and this resulted in my experiments with my conversion formula to sometimes give results that did not quite agree (although only in the ninth or tenth decimal place). Inv ln(1) is much more accurate (not to say simpler) and consistently gives the correct result, thank you very much.
 2005-08-14, 06:29 #6 Glenn Leider     Aug 2002 Carlsbad, Calif. 3710 Posts I like "1 Inv ln" for e too. As for a quicker converging expression than 1 + 1/1! + 1/2! + 1/3! + 1/4! + ... + 1/12! try 1 + 2/1/1 - 2/1/7 + 2/7/71 - 2/71/1001 + 2/1001/18089 - 2/18089/398959 + The pattern: 1 + 6x1 = 7, 1 + 10x7 = 71, 7 + 14x71 = 1001, 71 + 18x1001 = 18089, 1001 + 22x18089 = 398959, etc. It's based on this continued fraction: e = 1 + 2/(1 + 1/(6 + 1/(10 + 1/(14 + 1/(18 + 1/(22 + ...)))))) Last fiddled with by Glenn Leider on 2005-08-14 at 06:37

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