AlgebraIIChapter7TestReview
1. Usepropertiesoflogarithmstoexpandeachlogarithmicexpressionasmuchaspossible.Where
possible,evaluatethelogarithmicexpression.
a. log ! 125𝑥 ! 𝑦 b. log ! (
!
!
!"
)
2. Solveeachequation.
a. 25!!!! = 625 ! b. 𝑒 !!! = 52
c. 3 𝑙𝑜𝑔 1 − 2𝑥 = 6
d. 𝑙𝑜𝑔8 − 𝑙𝑜𝑔2𝑥 = −1
e. log 𝑥 + 21 + 𝑙𝑜𝑔𝑥 = 2
f.
ln 𝑥 + 2 − ln 𝑥 − 6 = ln 8 g. Supposethepopulationinacountryiscurrently8,100,000.Studiesshowthiscountry’s
populationisincreasing2%eachyear.
i. Whatexponentialfunctionwouldbeagoodmodelforthiscountry’s
population?
ii. Usingtheequationyoufoundinparti,howmanyyearswillittakeforthe
populationtoreach9million?Roundyouranswertothenearesthundredth.
h. Suppose$5000isputintoanaccountthatpays6%compoundedcontinuously.How
longwillittaketodoubleyourmoney?
AlgebraIIChapter7TestReview
3. Graphthefollowingfunctions.
i. Statethevertical/horizontalasymptotes.
ii. Statethedomainandrange.
iii. ProvideatableofvaluesORlabelatleast4pointsonyourgraph.
iv. Tellhowthefunctionwastransformedfromtheparentfunction𝑓 𝑥 = 2 ! a. 𝑔 𝑥 = 4 + 2 !!! \
b. ℎ 𝑥 = log ! (𝑥 − 2)