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Section 4.5 Logarithmic and exponential functions

by: Emmaline Murphy

Section 4.5 Logarithmic and exponential functions MAC 1140

Marketplace > Florida State University > Mathematics (M) > MAC 1140 > Section 4 5 Logarithmic and exponential functions
Emmaline Murphy

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About this Document

4.5 notes for precal
Precalculus Algebra
David Ekrut
Class Notes
25 ?




Popular in Precalculus Algebra

Popular in Mathematics (M)

This 4 page Class Notes was uploaded by Emmaline Murphy on Tuesday March 1, 2016. The Class Notes belongs to MAC 1140 at Florida State University taught by David Ekrut in Spring 2016. Since its upload, it has received 25 views. For similar materials see Precalculus Algebra in Mathematics (M) at Florida State University.


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Date Created: 03/01/16
Section5LogarithmandExponentiEquations 1. TrrFoRM au aP Ithe equation can be resoithaitisintheformau: a'thenwe can changehitou,:'t). 4 "* Example l.lFi,nilsuc11ro116{z-*} \V= 2 ' 8r] r (t -x)= n A _) )a J.3 4+ 21 An A 2222 22 4te* x) = 3 *4x* * ?r *4Y = -5 A=S - + Example 1.2Findalr suc71ro"3-2*::) a" )x :c -l o *t tfb-?x =t* 3 'A',v -l I -1 -4 -AX.-, " r/f, d., X,e Sect4.5 2. TneFoRM a,ulf Itheequatiocan brewrittsothaitis the forau: brthenwe... (1takethe natural logof botsides, (2usetheproperlna": u,lnat (3Solvefor tvariabby (a) multiply out (b)add/subtrsotaltermswitthe variabare oone siand other terms othe othside (c) facout thvariable (ddivide (eusethepropertof logarittorewrittomatcthe solution Example 2.1Fi.nal* sucth,aB,-1 42-* - (1)2 (2).*14 tr@ilW lIt ,.4n1 (s)tn2 (rf^ 3 ={2_x} (44 XIN 8- ln #; Qtn4* xtnl (5)Lr^4 *xl n4 fxlh4 (b),n48 xlnS+xi n4-1 ns z etn* 1nn +1n3 *Itn3 + .r )\n 3 + J{ih4 : f; t*",4 + in? +rn4) f + tn3 x(th3 atrn4 x(\h? +t4q)= ln4'+ \n? \---'re*_*_*-_4 *(w; :* --1L'-*:/". {;"ri-il;"$) \n3+\n$ Sect4.5 Example 2Fi,nallsucthat e2'-3 *x-? a Ve: I lM =1 Wi? :lrj+ * ail lx*t= ll",t {' I lvr{ tff lr,frf 3.TnpFoRMlog,u:logou: =*f= 1n.'".ft*$= Ifthe equacan re*rittenhe folog*'loo, thwe cachange rhis to?).p6ptArlr.,,h ly ? U > a Exampl3.1.i,nalri3tog,-:logq2lX 76 \orj -) qq*, =lDq o(4 t Q5)"* -) 0^,;)u/^= x=! e>r'* :) i x=la5''' ,4[]! Example 3Fi,natrrbtr:::r-r"f lrf , :6_S=r12 dh I** Y = le *1 twV*,t*&tug .sDl(*r * -l:- t2 / nH- A sotuti*ro4 x"^"k*l?: 0 -); Soltx-h nrr (x+4'Xx-3 r o X= -1 x=S Sect4.5 4.TlteFoRMlagou:b LL:&b.equation can betten iformog'u,:,thewe can chathis to Example 4.Find",fP *: -Z 3A _l <\ togxG;=)i -> i: i* = = (a") \-/ ^a ie = o-e')-' xd= a- ,/t y;,. tr*f (# =)-' c x,- J '= !A'* Gu) Example 4.Fi,ndi,logrr($)-2 r, -"x 3e b;)r = (*.e- )* = Jc{ -' 3*-#, S# *)-- H=b x+; r lb= fi-ta (Vy#r x-4 todtqrx+a) 't$-*{L}3- tfrrtqt'4 )f-+t=lddi .*) \01 +a) - t![s#i#) = tCx = t X1-;= tUX *$*< ),t* =. *""{* : tog+(r+a) irqo{x;-4)- *-*::-}i"Fr i t1.- 1;'A-


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