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Properties of Exponents and Logarithms

Prop ertiesofExp onentsandLogarithmsExp onentsLetaandbb erealnumb ersandmandnb ertiesofexp onentshold,providedthatalloftheexpressio nsapp earinginaparticularequationarede +n2.(am)n=amn3.(ab)m= n,a6=05. ab m=ambm,b6= m=1am,a6= ,a6= npa mwheremandnareintegersinprop nition:y=logaxifandonlyifx=ay,wherea> ,logarithmsareexp : logxalwaysreferstologbase10, ,logx=log10x. lnxiscalledthenaturallogarithmandisusedt orepresentlogex,wheretheirrationalnumb ere 2 ,lnx=yifandonlyifey=x. :logba= ertiesofLogarithms(Recallthatlogsareonly de nedforp ositivevaluesofx.) + + ,foralla> 1= ,foralla>01

ln x is called the natural logarithm and is used to represent log e x , where the irrational number e 2 : 71828. Therefore, ln x = y if and only if e y = x . Most calculators can directly compute logs base 10 and the natural log. orF any other base it is necessary to use the change of base formula: log b a = ln a ln b or log 10 a log 10 b.

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Transcription of Properties of Exponents and Logarithms

1 Prop ertiesofExp onentsandLogarithmsExp onentsLetaandbb erealnumb ersandmandnb ertiesofexp onentshold,providedthatalloftheexpressio nsapp earinginaparticularequationarede +n2.(am)n=amn3.(ab)m= n,a6=05. ab m=ambm,b6= m=1am,a6= ,a6= npa mwheremandnareintegersinprop nition:y=logaxifandonlyifx=ay,wherea> ,logarithmsareexp : logxalwaysreferstologbase10, ,logx=log10x. lnxiscalledthenaturallogarithmandisusedt orepresentlogex,wheretheirrationalnumb ere 2 ,lnx=yifandonlyifey=x. :logba= ertiesofLogarithms(Recallthatlogsareonly de nedforp ositivevaluesofx.) + + ,foralla> 1= ,foralla>01


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