SECT 2.2WHAT IS A LOGARITHM?
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I) LOGARITHMS:
A logarithm function is an “inverse” of an exponentialfunction
x
y
-4
-3
-2
-1
0
1
2
3
4
-4
-3
-2
-1
1
2
3
4
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HOW DO LOGS WORK?
The “LOG” of annumber will give
you the exponentwhen it has a base of 10
The purpose of“LOG” is to thefind the exponent
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II) LOGS WITH OTHER BASES:
Logarithms can be used to find the exponent with any bases
Base
Number
Exponent
The “LOG” of an numberdivided by the “LOG” ofthe base will give you theexponent
The purpose is to thefind the exponent
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III) GENERAL RULES WITH LOGARITHMS:
i) You can never “LOG” a negative number
ii) The “LOG” of one is zero
iii) Changing from “Exponential form” to “LOG form”
iv) When no base is present, then the base is 10
Base
Number
Exponent
Exponent with
Base of 10
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IV) SOLVING LOGS WITHOUT A CALCULATOR
Check:
Check:
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EX: THE POPULATION IN CANADA IS INCREASING ATAN ANNUAL RATE OF 3.5%. IF THE CURRENTPOPULATION IS 20 MILLION, WHEN WILL THEPOPULATION REACH 50 MILLION PEOPLE?
The population of Canada will
reach 50 million approximately
27 years
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PRACTICE: TOM IS DEPOSITING $5000 IN A SAVINGSACCOUNT THAT PAYS 3% INTEREST COMPOUNDED SEMI-ANNUALLY. HOW LONG WILL HE NEED TO KEEP THEMONEY IN THE BANK TO ACCUMULATE $10,000?
Gather information!!
Plug into formula
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HOMEWORK:
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