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

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

Use the properties to verify

ln 24 (3ln 2 ln3)

Use the properties to fully expand

log10z

Use the properties to fully expand2

ln xyz

Use the properties to fully expand2

2log ( 2)x x

Use the properties to condense to a single logarithm

5 5 5log 8 log logx y

Use the properties to condense to a single logarithm

2ln 7 3ln x

Use the properties to condense to a single logarithm

2[log log( 1) log( 1)] log( )x x x x

Given logx2 = 3.28 and logx3 = 4.02 and logx5 = 5 . Find logx1.2