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## Section 4.4 Properties of Logarithmic functions

by: Emmaline Murphy

26

0

4

# Section 4.4 Properties of Logarithmic functions MAC 1140

Marketplace > Florida State University > Mathematics (M) > MAC 1140 > Section 4 4 Properties of Logarithmic functions
Emmaline Murphy
FSU

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4.4 notes for precal
COURSE
Precalculus Algebra
PROF.
David Ekrut
TYPE
Class Notes
PAGES
4
WORDS
CONCEPTS
precal
KARMA
25 ?

## 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 26 views. For similar materials see Precalculus Algebra in Mathematics (M) at Florida State University.

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Date Created: 03/01/16
1.Sscrrolr.4PnoppRTrESop LocaruTnMrc FuNcrroNs (1)Recallhe definitianlogarithm: logr : yitandonly7aP: r (2)Specialogarithmsushoulduicklrecognizand/oevaluate: 0\ rog,r":, ["] log,a:1 I Xo*', x0 x l(b) I rlnx I ,";:ro*roz I : lnX I,u,tor:to""J I L' EXPONTNITIATIN\ft Example 1,.LSoluforA,lny: r- 41n2. -4 lne : I t Iny x- 1ln2 : ln )4 E. ln lb w 0 Y -4lnL y= (r" ,(,, I Y ln tv \/ = .a- 4rvl J_x\ tx = .0, . = -lre' Y= lae (3)Sincf(*): a'andS(*):logorare one-to-one: =7 (u) o" a?ifandonlylu : u ,tr. (b)l"su : trsgifand ontyu,: EX p0Nfn liINTg :ln(r Example 1.2.Solaforg:lng - 16). ^ tny -ln(x-l*) O =& clurn&tn : ftk,"W) :) Y ' x'lh x> lb Section 2 (4Sinfe*) anallLd)lograrinverofeach other: (a)Ioo,u'tl (b)ar"s"u ExamplL.3.ualuate ezusi,ngoperoetponents. 2tn\t lnT ln4i+ t*S In 1b i*# O = O = U 'O : lb.fi s 10 (5Operations: : (a)Lag"(mn1om,*Iogon \_. lllff"[ll:",ii*;_,.s"n Example LEualuaezb{tus'ithaboueoperti,es. * +ln3 ,,tn tl^ ,e) r1tna9* q b oln4 =8- =e Example LErpand, asasuchsdt"ff .4 +octoK *7 t +t'4'rfl,s rn l*G*)r \$h{v-,f}- rn(ti:") tnft') W = *S lr"i = iln.y + * t"V- l J lhtr.r L Sec,4.4n 3 Example1-.Rewri,tesinglelogarita*(" 1)+2log(3+2) 31ogc -r - - (gx+il^ OryT ExampleL.7.f logaa:andlogaSb, thenlo--t9 (azab lol,r\B = loqq2'b'3 (babz (c2(+ b) =loql(J.3)' (d,) @( a+bz =toiqte+lo4q3 7 ''l%lA + &1,01+ = cL + Zb- 4 ExampleL.8Sotrfory:,.y:lnr_41n, : Iny _ ln 2 +lny lny= l"Go) D0 l'-{6t-uu e{/ X (x >o) 4 j = rt" Section4 4 :W. (6)ChangeofbaseormulaIfb>0 andb+ 0,thenlogr Inparticular, logor:*:;: H;. Example L.9Rewrifeog35withbase usi,changeofbasformula. lWtS = + chw'qp, bttw bpsq 'tg't, ln ',ffi 'A) I +r*{.P*' {\ {"): losorisonldefinedora} 0,a* 1,andr> 0. Example \.LO.Forthefollowi,ngrlnll,U>0 andylL. Tnteor [alse? (a)tos*t:o tntg Xo . I r"*ny:tosr.loss P F6{ l-tO r togx + wqy 9ror,":'# trelSO hpq t 104Y (d)tos_:,logr VCt\|e/ /yrcga -- ! roqx - loqy : (elosoS-3 -3 tfUt"f,., (fr"s-r?5)':3 €ASgt t Y^ronr {,(,al [o5ti,,t+ a\8, f,t,Lt\$t ,vf'(.) + b vf* \dlrr't

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