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7.4 Properties of Logarithms

7.4 Properties of Logarithms. Review: Properties of Exponents . 3 2 * 3 7. Product Property. The logarithm of a product is equal to the sum of the logarithms of the factors. Example: log 3 729 = log 3 (27 * 27) = log 3 27 + log 3 27 log b mn = log b m + log b n.

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7.4 Properties of Logarithms

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  1. 7.4 Properties of Logarithms

  2. Review: Properties of Exponents • 32 * 37

  3. Product Property • The logarithm of a product is equal to the sum of the logarithms of the factors. • Example: log3 729 = log3(27 * 27) = log3 27 + log3 27 • logbmn = logbm + logbn

  4. Quotient Property of Logarithms • The logarithm of a quotient is the logarithm of the dividend minus the logarithm of the divisor • log4 (16 ÷ 2) = log4 16 – log42 • logb(m÷n) = logbm – logbn

  5. Power property of Logarithms • Let’s try this one: log 103 (use the product property. • logbap = plogb a

  6. Inverse Property of Logarithms • How do you solve something like 2x – 5 = 9? • Use inverse operations. • So, how do you “undo” a log? An exponential? • logbbx = xblogbx=x

  7. Some problems • Simplify: log 100.9 • 2log2(8x) • log883x+1

  8. Change of Base Formula

  9. Express as a single logarithm. Simplify, if possible. • log550 + log5 62.5 • log 100 + log 1000 • log3 3 + log327

  10. Simplify and evaluate • log4320 – log45 • log 5.4 – log 0.054 • log6496.8 – log62.3

  11. Simplify • log882 • log335 • log7493 • log1/2(0.25)4

  12. Simplify • log22x+5 • 2.5log2.519 • log41024 • log2(0.5)4

  13. Evaluate • log9(1/27) • log832 • log510 • log227

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