Properties of Logs Objective: Be able to use the properties of logarithms to expand and condense...
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Transcript of Properties of Logs Objective: Be able to use the properties of logarithms to expand and condense...
![Page 1: Properties of Logs Objective: Be able to use the properties of logarithms to expand and condense expressions. TS: Make decisions after reflection and review.](https://reader036.fdocuments.in/reader036/viewer/2022082510/5a4d1afe7f8b9ab059985b01/html5/thumbnails/1.jpg)
Properties of LogsObjective: Be able to use the properties of logarithms
to expand and condense expressions.TS: Make decisions after reflection and reviewWarm-Up:1) Use the change of base formula to rewrite loga7 as a
ratio of (a) common logs and then (b) as a ratio of natural logs
2) Use your calculator to find log20130
![Page 2: Properties of Logs Objective: Be able to use the properties of logarithms to expand and condense expressions. TS: Make decisions after reflection and review.](https://reader036.fdocuments.in/reader036/viewer/2022082510/5a4d1afe7f8b9ab059985b01/html5/thumbnails/2.jpg)
Properties of Logarithms
logbx + logby = __________
logbx – logby = __________
logbxa = ____________
Likewise…ln x + ln y = ln (xy)ln x – ln y = ln (x/y)lnxa = a(ln x)
And don’t forget about Change of Base!
loglog lnloglog ln log
cb
c
aa aab b b
![Page 3: Properties of Logs Objective: Be able to use the properties of logarithms to expand and condense expressions. TS: Make decisions after reflection and review.](https://reader036.fdocuments.in/reader036/viewer/2022082510/5a4d1afe7f8b9ab059985b01/html5/thumbnails/3.jpg)
Use the properties to verify
ln 24 (3ln 2 ln3)
![Page 4: Properties of Logs Objective: Be able to use the properties of logarithms to expand and condense expressions. TS: Make decisions after reflection and review.](https://reader036.fdocuments.in/reader036/viewer/2022082510/5a4d1afe7f8b9ab059985b01/html5/thumbnails/4.jpg)
Use the properties to fully expand
log10z
![Page 5: Properties of Logs Objective: Be able to use the properties of logarithms to expand and condense expressions. TS: Make decisions after reflection and review.](https://reader036.fdocuments.in/reader036/viewer/2022082510/5a4d1afe7f8b9ab059985b01/html5/thumbnails/5.jpg)
Use the properties to fully expand2
ln xyz
![Page 6: Properties of Logs Objective: Be able to use the properties of logarithms to expand and condense expressions. TS: Make decisions after reflection and review.](https://reader036.fdocuments.in/reader036/viewer/2022082510/5a4d1afe7f8b9ab059985b01/html5/thumbnails/6.jpg)
Use the properties to fully expand2
2log ( 2)x x
![Page 7: Properties of Logs Objective: Be able to use the properties of logarithms to expand and condense expressions. TS: Make decisions after reflection and review.](https://reader036.fdocuments.in/reader036/viewer/2022082510/5a4d1afe7f8b9ab059985b01/html5/thumbnails/7.jpg)
Use the properties to condense to a single logarithm
5 5 5log 8 log logx y
![Page 8: Properties of Logs Objective: Be able to use the properties of logarithms to expand and condense expressions. TS: Make decisions after reflection and review.](https://reader036.fdocuments.in/reader036/viewer/2022082510/5a4d1afe7f8b9ab059985b01/html5/thumbnails/8.jpg)
Use the properties to condense to a single logarithm
2ln 7 3ln x
![Page 9: Properties of Logs Objective: Be able to use the properties of logarithms to expand and condense expressions. TS: Make decisions after reflection and review.](https://reader036.fdocuments.in/reader036/viewer/2022082510/5a4d1afe7f8b9ab059985b01/html5/thumbnails/9.jpg)
Use the properties to condense to a single logarithm
2[log log( 1) log( 1)] log( )x x x x
![Page 10: Properties of Logs Objective: Be able to use the properties of logarithms to expand and condense expressions. TS: Make decisions after reflection and review.](https://reader036.fdocuments.in/reader036/viewer/2022082510/5a4d1afe7f8b9ab059985b01/html5/thumbnails/10.jpg)
Given logx2 = 3.28 and logx3 = 4.02 and logx5 = 5 . Find logx1.2