LOGARITHMS Logs

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LOGARITHMS(Logs)

• IA

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What is a Log ???

• LOGARITHM is an exponent.  
• It is the exponent to which the base must be
  raised to produce a given number.

• For example, since
• 2³   8
• then 3 is called the logarithm of 8 with base 2.
  
• 3 is the exponent to which 2 must be raised to
  produce 8.

3

• 10³ 1,000
• then

• 3 is the exponent to which 10 must be raised to
  produce 1,000.
• The logarithm of 1,000 with base 10 is 3.

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DEFINTION What we know so far

• If
• Then ,

• For example,
• 25 5² (expo form)
• (log form)
• 81 34 (expo form)
• (log form)
• 100 3x (expo form)
• (log form)

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Common Logs Evaluating Logs

• A common log is a logarithm that uses base 10.
• You can write
• as log y
• But,
• IS NOT log x

• EVALUATING LOGS
• Evaluate
• set x
• by definition, we have
• 10x 100
• so x must be 2.

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NOW WE LEARN TO SIMPLIFY LOGs

• There are just 3 log properties to know
• LETs INVESTIGATE !!!
• To do this GRAB A CALCULATOR!

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PRODUCT RULE

• log 8 log 3
• log 10 log 2

• log 24
• log 20

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First rule

• log a log b log(ab) (assume base10)
• Same bases only!

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QUOTIENT RULE

• log 20 log 4
• log 9 log 3
• log 7 log 20

• log 5
• log 3
• log (7/20)

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Second Rule

• log a log b log a/b (assume base10)
• Same base only!

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POWER RULE

• log 15²
• log 74

• 2 log 15
• 4 log 7

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Third Rule

• log ap ? p log a (assume base10)