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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