Logs - Revision history

Iwiseman: /* Second Time around */

2026-04-19T01:19:01Z

Second Time around

← Older revision		Revision as of 01:19, 19 April 2026
Line 41:		Line 41:
	Note the logs obtained were via a logarithm book to 4 significant figures. Using accurate logs e.g. 37 = - 1.568201724… will result in rounding errors.<br>		Note the logs obtained were via a logarithm book to 4 significant figures. Using accurate logs e.g. 37 = - 1.568201724… will result in rounding errors.<br>
	<br>		<br>
	Convert 10³.³³⁹¹ back to a natural number and you get ≈ 2183		Convert 10³.³³⁹¹ back to a natural number and you get = 2183<br>
	~~(the small difference from 2183~~ is ~~rounding in~~ the ~~logs)~~.		<br>
			Below is a screenshot of the old antilogarithms table<br>
			[[File:Log tables.png]]

2026-04-19T01:11:12Z

Second Time around

← Older revision		Revision as of 01:11, 19 April 2026
Line 39:		Line 39:
	3.3391		3.3391

	Note the logs obtained were via a logarithm book to 4 significant figures. Using accurate logs e.g. 37 = - 1.568201724… will result in rounding errors.		Note the logs obtained were via a logarithm book to 4 significant figures. Using accurate logs e.g. 37 = - 1.568201724… will result in rounding errors.<br>
			<br>
	Convert 10³.³³⁹¹ back to a natural number and you get ≈ 2183		Convert 10³.³³⁹¹ back to a natural number and you get ≈ 2183
	(the small difference from 2183 is rounding in the logs).		(the small difference from 2183 is rounding in the logs).

2026-04-19T01:09:11Z

Second Time around

← Older revision		Revision as of 01:09, 19 April 2026
Line 33:		Line 33:
	So when you add exponents, you are literally adding multiplicative distance.		So when you add exponents, you are literally adding multiplicative distance.
	That’s why log(a × b) = log(a) + log(b).		That’s why log(a × b) = log(a) + log(b).

	1.5682		1.5682
	+ 1.7709		+ 1.7709
	--------		--------
	3.3391		3.3391

	Note the logs obtained were via a logarithm book to 4 significant figures. Using accurate logs e.g. 37 = - 1.568201724… will result in rounding errors.		Note the logs obtained were via a logarithm book to 4 significant figures. Using accurate logs e.g. 37 = - 1.568201724… will result in rounding errors.

2026-04-19T01:08:51Z

Second Time around

← Older revision		Revision as of 01:08, 19 April 2026
Line 20:		Line 20:
	Well we convert this to be expressed as exponents		Well we convert this to be expressed as exponents
	10¹.⁵⁶⁸² x 10¹.⁷⁷⁰⁹		10¹.⁵⁶⁸² x 10¹.⁷⁷⁰⁹
	So now with exponents you can add them together to perform the maths. This works because ~~blahblah~~		So now with exponents you can add them together to perform the maths.<br>
			<br>
			This works because an exponent is the distance from 1 on a multiplicative number line. Each step is “multiply by the base”. So adding exponents is the same as multiplying numbers, and subtracting exponents is the same as dividing numbers.

			For example:
			2⁰ = 1 → 0 steps of ×2 from 1
			2¹ = 2 → 1 step of ×2 from 1
			2² = 4 → 2 steps of ×2 from 1
			2³ = 8 → 3 steps of ×2 from 1
			2⁴ = 16 → 4 steps of ×2 from 1

			So when you add exponents, you are literally adding multiplicative distance.
			That’s why log(a × b) = log(a) + log(b).

	So
	1.5682		1.5682
	+1.7709		+ 1.7709
	-------		--------
	3.3391		3.3391
	Convert ~~log~~ 10³.³³⁹¹ back to a natural number and you get 2183
			Note the logs obtained were via a logarithm book to 4 significant figures. Using accurate logs e.g. 37 = - 1.568201724… will result in rounding errors.

			Convert 10³.³³⁹¹ back to a natural number and you get ≈ 2183
			(the small difference from 2183 is rounding in the logs).

2026-04-19T00:21:54Z

Second Time Around

@@ Line 5: / Line 5: @@
 [[File:Logs1.png| 500px]]<br>
 '''Fold Change''' is defined as Ratio that describes a change in a measured value<br>
-=Second Time Around=
+=Second Time around=
-I want to restate this so I don’t forget it.
+So
 .5682
-+ 1.7709
+ +1.7709
---------
+ -------
 .3391
-```
+Convert log 10³.³³⁹¹ back to a natural number and you get 2183

2026-04-19T00:21:25Z

Second Time around

@@ Line 5: / Line 5: @@
 [[File:Logs1.png| 500px]]<br>
 '''Fold Change''' is defined as Ratio that describes a change in a measured value<br>
-=Second Time around=
+=Second Time Around=
-So
+I want to restate this so I don’t forget it.
 .5682
- +1.7709
++ 1.7709
- -------
+--------
 .3391
-Convert log 10³.³³⁹¹ back to a natural number and you get 2183
+```

2026-04-19T00:16:57Z

Second Time around

@@ Line 14: / Line 14: @@
   if you take the distance from 1 and 8, you can say 1 x 8 = 8 or 8 is 8 times bigger than 1
   if you take the distance from 1/8 and 1 is also 8 times the distance.
-So logarithms give you the magnitude of difference.
+So logarithms give you the magnitude of difference.<br>

2026-04-18T23:33:02Z

Second Time around

← Older revision		Revision as of 23:33, 18 April 2026
Line 10:		Line 10:
	To		To
	The logarithm of 8 in base 2 = 3		The logarithm of 8 in base 2 = 3
	Because ~~2U+00B3~~ is 8		Because 2³ is 8
			And 3 is how many times you need to times the base by to get the value. The above image is trying to convey that
			if you take the distance from 1 and 8, you can say 1 x 8 = 8 or 8 is 8 times bigger than 1
			if you take the distance from 1/8 and 1 is also 8 times the distance.
			So logarithms give you the magnitude of difference.

2026-04-18T23:12:40Z

Second Time around

← Older revision		Revision as of 23:12, 18 April 2026
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	So thought I might go around this again so I to not forget. The above information is probably the useful part of all this but a simple diagram demonstrates I do know this, I just forget.<br>		So thought I might go around this again so I to not forget. The above information is probably the useful part of all this but a simple diagram demonstrates I do know this, I just forget.<br>
	[[File:Logarithm explained.png \| 750px]]<br>		[[File:Logarithm explained.png \| 750px]]<br>
			To
			The logarithm of 8 in base 2 = 3
			Because 2U+00B3 is 8

2026-04-18T23:08:18Z

← Older revision		Revision as of 23:08, 18 April 2026
Line 7:		Line 7:
	=Second Time around=		=Second Time around=
	So thought I might go around this again so I to not forget. The above information is probably the useful part of all this but a simple diagram demonstrates I do know this, I just forget.<br>		So thought I might go around this again so I to not forget. The above information is probably the useful part of all this but a simple diagram demonstrates I do know this, I just forget.<br>
	[[File:Logarithm explained.png \| ~~500px~~]]<br>		[[File:Logarithm explained.png \| 750px]]<br>