8.3 Properties of Logarithms NOTES - Algebra 2 Common...
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© 2018 The Algebros, LLC Write your questions here! 8.3 Properties of Logarithms Use a calculator to evaluate each logarithm. Then match equivalent expressions from Column A with Column B. What do you notice? Column A Column B Product Property of Logarithms. Express each as a single logarithm. Connection to Exponents Expand the lograithm - Use a calculator to evaluate each logarithm. Then match equivalent expressions from Column A with Column B. What do you notice? Column A Column B Quotient Property of Logarithms. Expand the logarithm. Connection to Exponents Express as a single logarithm. NOTES
Transcript of 8.3 Properties of Logarithms NOTES - Algebra 2 Common...
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Writeyourquestionshere!
8.3PropertiesofLogarithmsUse a calculator to evaluate each logarithm. Thenmatch equivalent expressions from ColumnAwithColumnB.Whatdoyounotice?ColumnAColumnBProductPropertyofLogarithms.Expresseachasasinglelogarithm.ConnectiontoExponents Expandthelograithm-Use a calculator to evaluate each logarithm. Thenmatch equivalent expressions from ColumnAwithColumnB.Whatdoyounotice?ColumnAColumnBQuotientPropertyofLogarithms.Expandthelogarithm.ConnectiontoExponents Expressasasinglelogarithm.
NOTES
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ColumnAColumnBPowerPropertyofLogarithms.Expandthelogarithm.ConnectiontoExponents Condensethelogarithm.DefinitionBasedPropertiesRecall: 8)SimplifyChangeofbaseformula:Watchmedothisone! Pauseandyoutrythisone
SUMMARY:
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8.3PropertiesofLogarithms
DIRECTIONS:ExpandeachLogarithm.1) log! 3𝑥 2)log!
!! 3)log! 3ℎ!
4)log!!"! 5)log 5𝑡 !!! 6)ln 2ℎ
DIRECTIONS:Condenseeachlogarithm.7)log! 6 + log! 2 8)log! 8 − log! 𝑥 9)!
!log! 𝑥
10)4 ln 𝑥 + ln 5 11)log! 6 + log! 𝑦 − log! 2 12)3log 𝑥 − 2 log 𝑦 − log 𝑧
DIRECTIONS:Simplify.13)log! 40 + log! 25.6 14)log! 81! + log! 6!! 15)log! 60 + log! 12.8 − log! 6
16)log!!! 𝑥 − 3 ! 17)log!!! 𝑥! + 4𝑥 + 4 ! + log! 5 18)log! 27 + log! 54 − log! 2
PRACTICE
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Solve. Express your radical solutions in the simplest form.
19) (3𝑦)! + 10 = −18
20) (2𝑡 + 3)! + 39 = 3
8.3PropertiesofLogs
DIRECTIONS:ExpandeachLogarithm. DIRECTIONS:Simplify.
1)log!!!!
! 2)log 250 + log 6 − log !
!
3)EveryyearSullybuys130redpensforgradingatthebeginningoftheyear.Hefiguresthatthenumberofpensdecreasesexponentiallyatabout9%eachweek.Whenheonlyhas10lefthegoesandbuysmore.a)Setupanexponentialequationforthegivensituation.b)Rewritetheequationasalogarithm.c)ExpandyourlogarithmusingPropertiesofLogarithms.d)HowmanyweeksuntilMr.Sullivanneedstobuymorepens?
WRAP UP
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4)7kidsonthebasketballteamreturnsickfromaweekendplayinggamesatLakenheathHighschoolwithavirus.Theaggressivevirusspreadsat130%eachday.Howlongmanydaystill500studentsaresickatschool?5)Mr.Kellyistryingtoteachhissiblingsaboutsavingmoney.Hegiveseachofhissibling$1000toinvest.DougieKelylikestoplayitsafesoheputshismoneyinaSavingsAccountthatgivesincreaseshisaccountexponentiallyat2%ayear.Hewantstosave$5000.a.HowlongwillittakeDougietohave$5000inhisaccount?b.SisterSaraKellyisabitmoreofarisktaker.ShedecidestoputhermoneyinthestockmarketbecauseshefoundthatsheMIGHTbeabletoget12.5%interest.HowmuchlongerwillDougiehavetosavetogetto$5000?EXIT TICKET –
Using complete sentences, take a look at WRAP UP questions 3-5 and explain how the properties and definitions of logarithms are useful in solving exponential equations.
SMP#3SMP#3
