Logarithmic Functions - Revision history

Lila: /* Resources */

2021-10-21T20:47:24Z

Resources

Lila at 17:32, 4 October 2021

2021-10-04T17:32:54Z

Lila: /* Logarithmic Functions */

2021-10-04T17:32:00Z

Logarithmic Functions

Lila: /* Logarithmic Functions */

2021-10-04T17:31:03Z

Logarithmic Functions

Lila at 17:28, 4 October 2021

2021-10-04T17:28:47Z

Lila at 15:31, 15 September 2021

2021-09-15T15:31:54Z

Johnraymond.yanez: Created page with "* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_Functions.pdf Logarithmic Functions], Book Chapter * [https://mathresearch.uts..."

2020-08-17T14:24:22Z

Created page with "* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_Functions.pdf Logarithmic Functions], Book Chapter * [https://mathresearch.uts..."

New page

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_Functions.pdf Logarithmic Functions], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_FunctionsGN.pdf Guided Notes]

← Older revision		Revision as of 20:47, 21 October 2021
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	* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_Functions.pdf Logarithmic Functions], Book Chapter		* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_Functions.pdf Logarithmic Functions], Book Chapter
	* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_FunctionsGN.pdf Guided Notes]		* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_FunctionsGN.pdf Guided Notes]
		+
		+	== Licensing ==
		+	Content obtained and/or adapted from:
		+	* [https://en.wikibooks.org/wiki/A-level_Mathematics/OCR/C2/Logarithms_and_Exponentials Logarithms and Exponentials, Wikibooks: A-level Mathematics/OCR/C2] under a CC BY-SA license

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 A '''logarithmic equation''' is an equation wherein one or more of the terms is a logarithm.
-e.g. Solve <math>\lg x + \lg (x+2) = 2</math> <ref group="note"><math>\lg</math> is another way of writing <math>\log_{10}</math></ref>
+e.g. Solve <math>\log x + \log (x+2) = 2</math> (<math>\log</math> is another way of writing <math>\log_{10}</math>).
 <math>\begin{align}
-\lg x + \lg (x+2) &= 2 \\
+\log x + \log (x+2) &= 2 \\
-\lg (x(x+2)) &= 2 \\
+\log (x(x+2)) &= 2 \\
 x(x+2) &= 100 \\
 x^2 + 2x &= 100 \\

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 In mathematics you can find the inverse of an exponential function by switching x and y around:
 <math>y = b^x\,</math> becomes <math>x = b^y\,</math>. The problem arises on how to find the value  of y. The logarithmic function solved this problem. All conversions of logarithmic function into an exponential function follow the same pattern: <math>x = b^y\,</math> becomes <math>y = \log_b x\,</math>. If a log is given without a written b then b=10. Also with logarithmic functions, b > 0 and <math>b \ne 1</math>. There are 2 cases where the log is equal to x: <math>\log_bb^X = X\,</math> and <math>b^{\log_bX} = X\,</math>.
 ===Laws of Logarithmic Functions===

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 ===Change of Base===
 When x and b are positive real numbers and are not equal to 1. Then you can write <math>\log_a x\,</math> as <math>\frac { \log_b x}{ \log_b a}</math>. This works for the natural log as well. here is an example:
 <math>\log_2 8 = \frac { \log 8}{ \log 2} = \frac {.9}{.3} = 3\,</math> now check <math>2^3 = 8\,</math>

← Older revision		Revision as of 15:31, 15 September 2021
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		+	==Resources==
	* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_Functions.pdf Logarithmic Functions], Book Chapter		* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_Functions.pdf Logarithmic Functions], Book Chapter
	* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_FunctionsGN.pdf Guided Notes]		* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_FunctionsGN.pdf Guided Notes]

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 ==Resources==
 * [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_Functions.pdf Logarithmic Functions], Book Chapter
 * [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_FunctionsGN.pdf Guided Notes]