Properties of Logs - MCCC
Solutions to Properties of Logs
1. Definition [pic]
Forward: Solve for an exponent
EX: Find the inverse for [pic]so y-1=log3x
EX: The How long will it take for an investment to double at 5% about 13 years
Reverse: Get rid of a log
EX: Find x if 3 = lnx x = e3
2. Sum/Product Property [pic]
Forward: Combine a log
EX: Find a single log for log2+log5= log 10 = 1
EX: Find x if log2+logx =3 log (2x)=3 so 2x=103 =500
Reverse: Find the components of a log
EX: If log2=.3 find log 20=log(10*2)=log10+log2=1+.3
3. “Ladder” Property [pic]
Forward: Get rid of a coefficient
EX: Find 3log4+2log5=log43+log52 =log(43*52)
Reverse: Get rid of an exponent inside a log
EX: Find [pic]=5000 log28=5000*3=15,000
4. Change of Base [pic]
Forward: Evaluate a old bases in terms of a new one
EX: Find [pic]=ln4/ln3=1.26…
EX: Graph [pic] use y1=log(x)/log(3)
Reverse: Divide logs of a same base to get a single log
EX: Simplify lnx/ln10 = log(x)
5. Log of Both Sides [pic]
Forward: Take the log of both sides
EX: Derive the change of base formula [pic]
Reverse: Drop the logs from both sides
EX: If logx=log4 find x. x=4
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