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Section 4.3 Logarithmic Functions

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by: Emmaline Murphy

Section 4.3 Logarithmic Functions MAC 1140

Marketplace > Florida State University > Mathematics (M) > MAC 1140 > Section 4 3 Logarithmic Functions
Emmaline Murphy

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About this Document

4.3 notes for percale
Precalculus Algebra
David Ekrut
Class Notes
25 ?




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This 9 page Class Notes was uploaded by Emmaline Murphy on Monday February 29, 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 21 views. For similar materials see Precalculus Algebra in Mathematics (M) at Florida State University.


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Date Created: 02/29/16
1.SpcuoN 4.3LocanITHMIC FuNcuoNs Definition.A.The losarithofruith, respertlr.e baisdefi,ned, by g:logo* iand,ontya1 X = OX Example L.t.Rewri,tei: ro,s{l,logarithm. loqrrTL Example 1.2.Reuritelogr(r +): 3asan erponent. (ilu= x+t Example L.3.logo7: C qo = I Example 1.4.logoo: I a'-- a 2.LocanrruMs v.s.ExPoNENTS (1)al"s"' X (2)logo': X Example 2.!.Eaaluatelogtrqlffi)a - I (2) q= W* sew_fr Example 2.2,Si.mpt (0.S)t"sg{i+=) t + [ 5#*$tq# Section 4.3 3.Evar,uarrLocARrrHMs Example3.1.Eualuaeaclogarithm. Nthord,ofoperations. fu)a+bg24 4+ )' 10fl^l 0 lol e \,n^*,1= = b (b)los2nn * (i)Log24a \ocl +1= 2,+4 to to1^?n)r ' i,q,f ra = ($-rig,1+1 B (j)(togrqa t toq, S : loga x : 3 '' '[,.0"q^et''(t d14 -tb o! A)+- (d,tas,a.( rcg ,+ *)-, a+) (*)tosr)= lota4-'' loqrb ( togr a),{ * r ?= 0 to4 *Q-*) = -'& ZIL I ta5efiq = 0ql1 .1 logr= -' ^'\ J 1 1 wlr?") \oq a 7 '"''4'tiug* *t 2") lofl+ 4 E = _t I -t =B (rnt g^| -t - Ios.4 a ; I (9/ +. 4& Section 4.3 4.Two SPECTALLocARTTHMS Def(1)fheCommon Logarithm:ogr: Iogror fheNatural Logaritlnr:Log.r @) -Y Example4.L. ,t!: 7 lnq, = Exampre 4.2.ros1000-: l1qtol000d= @q(o')* = l,j,o,r'* =vw Example 4.8.ehst: 5I {Et = 5.Tsp cRApH oF THELocARrrHMrc FUNCTToN (t)J(") lo8,zwherea> I l-$r.X It rstrO (z) : lo8*rwhereo o#t1';1,= the, t*,'r/f #{""fr= a-x f(r) < < Section 6.noppRTIps f(r) logowhere>1 r):los^rwhere0<o<1 Domain K] (a,oq) rr* b,d Range W Cro, s#) ffi,(-oo, o") Increasing rl N/A Decreasing N/A t.l Intercept(sx-lhT (r,o) (t,o) X- \i"tf n0 Y- thf no Y-thr AsS.mptote(s) V.A X=O V A. X=0 4.3 5 Section Exercis6.1.Matehthfuncti,on,tseph. Sls fr 7l (A) s:logrr {B)y:1og3(-r) (C) s - -Logrr (D)A:-logu(-r) C. 3' {. CT, Y--t%, Y= Ialri i-xi $) !1 t+. 3, J= l- t0ga 1= lo6J3 L-x) (6) D g= -tc$ell t% I 9= er- (7) (s) - {(r) GIru.SS r cn( Y="+ry) $= {t-"Yi G I rts( Y - crxrs 3' Sectionf.3 7. DolrarN Example 7.1. Find tlLe rlorno.irof f (.r): ln(.l 3er) - Example 7.2 . Fin,rl, th,rl,omain al : .1 3log.,(.r2 I G) - ) : Example 7.3. Fi,n,dthe d,om.a,in o.fQ) iog(l:2 - +) L. S'ecttolr.2ExpoNENTIAt FrnrcrroNs DefinitionL.L. An exponerntialfunetionisa janctiono,fhefann f (r): a* w.lreaei.a reanumber witha > 0and,aI 0. 2.Tns cnAprr oFTHE EXpoNENTTAL FUNCTToN (t)-f(") ot whereo > , {=Ax a> I A )=0 [+ (z) : a* where 0< s< 1 "f(r} x otaLl o Y= fl-,4 Section 4.2 3.PnopsnTtps .f*) a'wherc >1 f(*): o'wher0< a< 1 Domain fi, (-r",r") R (-no, eo) Range Wr (0, o.,) ff* (o,*) Increasing N/A lrl Decreasi:og tl N/A Intercept(s)Y- tnt ft, I y -rn+ (0, t) N0 - x-lht No *d* t,t| Asymptote(s) H A-Y=o 14 A. \=CI Section 4. MoncRAPHTNc Match the folequati:3*theirph:: (C)e ((D)yz-* (E)y:3*T tF)y:3*-' (G)u:3r-* (H)y:1-3' F c .-x- | -b* )= 2 Y= L-, A n l-X \= 3' )= c ft I _x r/= ? Y= t- (5) :3x- I Y: -3- (7)


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