fall 2019 math 1071 lecture notes 1.5 - wordpress.com

Section 1.5 Logarithms

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toga logbase a

Fuamplesa n 28 3 log x y t3b se 3T logan who knows

If a e write In x logen naturallogarithma co write log x logok

Rulestogaa I

10gal 0

togaKyl logacultlogacylogKyl login logay

logset yloycm

againlogyse

Toyachange f Base

logan ita

Domain of toga 0 too

Eaampies

a log nel log it logsett

m log 12 loycre4 Can't breakapartc log x3Cy lui log631 t logCytsel 310gCrit logly 1Kcel In yet he t Inge a he ekg a elmye jog.atogsY z1o93cseP

zeyd Domainof loy 2 se need 2 u o z x C w 2

e log ta log G91 91 7 9Solving logarithmic equations

Recall logaaku alofa se

Alwayscheck is equation definedfor solved seProblemsSolve fo se

a 3 8 1 9 8 3log 8

tlog3

Klog8 1 3

se 1 3

b Inre 243 Inco In n In 5 In toIn9 In toinfo

elate einfor

c log seen log set Eloy 64

log necku ill log64 elog 8

logCat I o6g8Helvie 11 8f i 82 9 0

N 3 Cut3 OCandidatesolutions x 3 3

Testof both workse 3

og 3 111log s il log4 log2

or 3log 3 1 logC 3 1 logC 21 logC f

NO BADOnly He 3 is a solution

d Howlong toget 100 if I invest 10 at 2 interestcompounded continuously

F PertF too too co e 002

t

P co yo ecooatr o oz co Ineo02t o.cat aeo.ozttC tuco lls yearso or