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Logarithms

Logarithms. Let’s Get It Started!!!. Remember. A logarithm is an exponent Every time you are working with logarithms, you can substitute the word exponent for logarithm,. The symbol for logarithm is log. What is written log 3 9. What is said log to the base 3 of 9 or

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Logarithms

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  1. Logarithms

  2. Let’s Get It Started!!!

  3. Remember • A logarithm is an exponent • Every time you are working with logarithms, you can substitute the word exponent for logarithm,

  4. The symbol for logarithm is log What is written log 3 9 What is said log to the base 3 of 9 or log base 3 of 9

  5. What does it mean???? log 3 9 means what power of 3 is 9?

  6. log 3 9 = 2 because 3 2 = 9 ^ ^ logarithmic form exponential form

  7. Write in exponential form: Logarithmic Form log 2 8 = 3 log 6 36 = 2 log 4 1 = 0 log 2 32 = 5 Exponential Form 2 3 = 8 6 2 = 36 4 0 = 1 2 5 = 32

  8. Exponential Form 3 0= 1 5 4 = 625 10 -1 = .1 6 3 = 216 Logarithmic Form log 3 1 = 0 log 5 625 = 4 log 10 (.1) = -1 log 6 216 = 3 Write in logarithmic form

  9. log a 1 = 0 because log a a = 1 because log a a x = x because a 0 = 1 a 1 = a a x = a x Special log values

  10. We interrupt the lesson on logarithms to bring you an important message… Hold on!! Let’s make sure you understand what “if and only if” means.

  11. A triangle is scalene if and only if the triangle has 3 sides of different lengths. The above statement takes the place of 2 statements: A triangle is scalene if it has 3 sides of different lengths. AND A triangle with 3 sides of different lengths is scalene.

  12. Now back to the lesson on logarithms…

  13. Definition The logarithm of x with base a (a > 0) is denoted by log a x and is defined as y = log a x iff a y = x if and only if

  14. y = log a x Replace the y with f (x) and you have a function f ( x ) = log a x

  15. log 5 25 = log 4 64 = log 2 64 = log 4 2 = log 3 (-1) = 2 3 6 ½ Impossible Why???? Evaluate:

  16. The log function with base 10 is called the commonlog function Your calculator uses base 10 when doing logarithms.

  17. log 100 = 2 because 10 2 = 100 If using common logs, you do not need to write in the base of 10.

  18. If you have any other base, to use your calculator, you can use the CHANGE OF BASE FORMULA: log a x =log x /log a

  19. log 4 7 = log 7 / log 4  1.404 Use your calculator to evaluate:

  20. Log 3 40 = log 40 / log 3  3.358

  21. log 3 543 = log 4 84 = log 2 79 = log 543 / log 3  5.732 log 84 / log 4  3.196 log 79 / log 2  6.304 More Examples using the calculator

  22. Graph f ( x ) = log 2 x Make a table of values x y

  23. Let’s review logarithms A logarithm is an exponent Calculators use base 10 To find log 5 399, using a calculator, use log 399 / log 5 (  3.72)

  24. The End!

  25. HOMEWORK TIME!!!

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