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Logarithm Question

 
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gothic5



Joined: 09 Jun 2014
Posts: 37

Posted: Thu Mar 02, 2017 12:13 am    Post subject: Logarithm Question Reply with quote

Does anyone know how to find the log of a negative number using a calculator?-Any Mathematical formulas I found online were too complex for me and I found nothing after a search for any videos explaining how to do this. Harold
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skyrack



Joined: 02 Aug 2012
Posts: 250
Location: Thailand

Posted: Thu Mar 02, 2017 9:13 am    Post subject: Reply with quote

The natural logarithm function ln(x) is defined only for x>0. So the natural logarithm of a negative number is undefined. The complex logarithmic function Log(z) is defined for negative numbers too.
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gothic5



Joined: 09 Jun 2014
Posts: 37

Posted: Fri Mar 03, 2017 12:19 am    Post subject: Reply with quote

Skyrack-Could I calculate the log for -4 by using certain keys on calculator?
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SteveGus



Joined: 19 Sep 2011
Posts: 47
Location: Southern Indiana

Posted: Fri Mar 03, 2017 6:06 pm    Post subject: Reply with quote

Logarithms are the opposite of exponents. For instance, the base 10 logarithm of 1000 is 3, because 10^3 = 1000. This means that there aren't really logarithms of negative numbers, because the exponential roots of negative numbers are all imaginary (i = SQR(-1)). Bear in mind also that x^-n = 1/x^n, which also suggests that n must be positive to avoid imaginary solutions.
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gothic5



Joined: 09 Jun 2014
Posts: 37

Posted: Wed Aug 25, 2021 2:54 am    Post subject: diurnal log question Reply with quote

In diurnal log motion table I see the diurnal log for 4 degrees is .77815.If I divide 4 degrees by 24 (using calculator) I get 10 minutes. Then log for 10 minutes calculator says -.77815.Same process for anywhere in this table with my calculator gives me a negative number equal to one in the table which is positive.Shouldn't the correct answer be positive? Request any help with this logarithm table which seems to be different than the one used above-Harold
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halw



Joined: 29 Jun 2021
Posts: 2
Location: Toronto

Posted: Wed Aug 25, 2021 4:39 pm    Post subject: logs Reply with quote

Nobody uses log tables for motion anymore.

I think you're confusing a negative logarithm, which exists, with the log of a negative number, which does not.

If it's the former, then you simple add it (as negative) to the other logs involved
(this is de facto division).

IF you had a problem like 666 x (-777), you could use logs if you ignore the sign and then re-attach it at the end. IOW add the positive logs of both numbers, find the antilog, THEN attach negative.
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gothic5



Joined: 09 Jun 2014
Posts: 37

Posted: Thu Aug 26, 2021 12:04 am    Post subject: diurnal logs Reply with quote

Although I know logs are not used often today.I still find them interesting.My question came from table 9 in back of Michelsons Table of Houses(diurnal log of 4 degrees) which is .77815.I think the answer to my original question lies in the Co-Log.Divide 4 degrees by 24 I get 10 minutes.The number 1 divided by 10 minutes is 6-and then the log for 6 or 6 minutes is .77815. This seems to be a different form than explained above by SteveGus and Skyrack.
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gothic5



Joined: 09 Jun 2014
Posts: 37

Posted: Thu Aug 26, 2021 7:10 pm    Post subject: diurnal logs Reply with quote

I wanted to correct myself in previous post where I wrote "The number 1 divided by 10 minutes is 6-and then the log for 6 or 6 minutes is .77815" This should be Log for 6 degrees not 6 minutes-So it seems that log 100=2 /1 button on a calculator.To find a diurnal or a ternary log requires a few steps.As also finding the colog of a number does.I would like to hear if there are any comments on diurnal and ternary logs and how they are different from general logs-Harold
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halw



Joined: 29 Jun 2021
Posts: 2
Location: Toronto

Posted: Thu Aug 26, 2021 9:24 pm    Post subject: Reply with quote

Keep in mind that logs, antilogs, etc are built into common calculators, and logs of trig functions are built into 10 dollar scientific calculators. Keep in mind that the base 10 log of any number less than 1 (and greater than O) is going to be negative.

I guess you're on a historical quest? Sort of like asking "How do I climb this mountain with the boots and gear that were available in 1920?" I note that you're also using a calculator with the logs, so this is like using brand new boots in your quest to climb the mountain with 1920 equipment!

I think the problem you're having is that the calculator gives the correct log, but the log table of time proportion omits the minus sign in my Michelson. This is OK, since the other minus signs are omitted in the other table, so you can add the two. IOW (analogously) (-2) plus (-1) = (-3). Note that the minus signs, *because they are everywhere* could be ignored.

Are you aware of the basic concept here? We want the increment to be added to a table entry for a planet. So we want to multiply the time interval/24 by the travel of the planet in the 24 hr period. So we will add logs. First, We look up in Table IX (Michelson American 1931-80) the log of the time interval (x hrs out of 24). Second, We look up the log of the daily motion, Table X (Michelson American Eph. 1931-80). Both are (fictively) positive. We add them, Third, then we use Table X backwards to find the increment. Fourth, we add the increment to the ephemeris earlier entry.

If the daily travel were negative, we'd modify the above slightly: At the fourth step, we'd subtract the increment.
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