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Properties Continued

Properties Continued. #5 – Product Law: log a xy = log a x + log a y. When adding two or more log expressions with the same base, combine them and multiply the arguments to form a new single log. Example. log 2 2 + log 2 5 = x log 2 (2x5) = log 2 10 = x log10 = x

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Properties Continued

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  1. Properties Continued

  2. #5 – Product Law:logaxy = logax + logay When adding two or more log expressions with the same base, combine them and multiply the arguments to form a new single log

  3. Example log22 + log25 = x log2(2x5) = log210 = x log10 = x log2 3.32 = x

  4. #6 – Quotient Law:logc(m/n) = logcm - logcn When subtracting two log expressions with the same base, combine them and divide the arguments to form a new single log. ORDER MATTERS!

  5. Example log333 - log311 = x log3(33/11) = x log33 = x x = 1(by property #2)

  6. Example log296 - log23 = x log2(96/3) = x log232 = x 2x = 32 x = 5(mentally or with calculator)

  7. Example log2(8/3) = log28 - log23 = 3 - log23 (since log28=3) = 3 – 1.58(since log23=1.58) = 1.42

  8. #7 –Law of Powers:logcxn = nlogcx When the argument has an exponent, that numbers because a coefficient to the log expression (and loses the exponent)

  9. Example log243 3log24 3(2)(since log24=2) So log243= 6

  10. Example 3log46 = log263

  11. Example log23√7 = log27⅓ = ⅓log27 = ⅓(2.81) = 0.94

  12. Example log7493 = 3log749 = 3(2)(since log749=2) = 6

  13. #8 – Change of Base Law:logcx = logx(we already know this one!)logc This is how we calculate logs on a calculator! (Remember we can use ln too!)

  14. Example log57 = x x = (log7/log5) x = 1.2

  15. Example 7x = 400 log7400 = x x = log400log7 x = 3.07

  16. HOMEWORK Workbook p.176 #7, 8 p. 177 #9, 12, 14 p. 179 #21, 25, 26 ***QUIZ on Monday on Exponents and Logs(open book!!) GO TO RECUP TOMORROW IF YOU NEED HELP!!!!!

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