4.3 - Properties of Logarithms

# 4.3 Properties of -

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<?xml version="1.0" encoding="utf-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title>4.3 - Properties of Logarithms</title> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link href=". ./m116.css" rel="stylesheet" type="text/css" /> </head> <body> <h1>4.3 - Properties of Logarithms</h1> <h2>Change of Base Formula</h2> <p>One dilemma is that your calculator only has logarithms for two bases on it. Base 10 (log) and base e (ln). What is to happen if you want to know the logarithm for some other base? Are you out of luck? </p> <p>No. There is a change of base formula for converting between different bases. To find the log base a, where a is presumably some number other than 10 or <em>e</em>, otherwise you would just use the calculator,</p> <p><strong>Take the log of the argument divided by the log of the base.</strong> </p> <p>log<sub>a</sub> x = ( log<sub>b</sub> x ) / ( log<sub>b</sub> a )</p> <p>There is no need that either base 10 or base <em>e</em> be used, but since those are the two you have on your calculator, those are probably the two that you're going to

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## This note was uploaded on 10/18/2011 for the course MAT 1033 taught by Professor Brown during the Spring '10 term at Valencia.

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4.3 Properties of -

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