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5.5 Objectives

5.5 Objectives. Apply the base properties of logarithms. Use the change of base formula. Properties of Logarithms. log a 1=0 and log a a =1 log a m+log a n = log a ( mn ) log a m-log a n = log a (m/n) log a ( m r )= rlog a m l n = log e (natural log). Change of base formula.

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5.5 Objectives

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  1. 5.5 Objectives • Apply the base properties of logarithms. • Use the change of base formula.

  2. Properties of Logarithms • loga1=0 and logaa=1 • logam+logan=loga(mn) • logam-logan=loga(m/n) • loga(mr)=rlogam ln = loge (natural log)

  3. Change of base formula • Let x, a, and b be positive numbers.. • ..where a≠ 1 and b≠ 1.

  4. Try these • ln 5+ ln 4 log 10-log 5

  5. And more… log 52 log 5 + log 15 – log 10

  6. 5.6 Objectives • Solve exponential equations • Solve logarithmic equations.

  7. Exponential Equations Basic form: Cax = k • Solve for ax • take the base a log of both sides, which makes the ax equal x because.. logaax = x • Solve the other side

  8. Try these Log (2x+1) =2

  9. Try these Log2 4x = 2-log2 x

  10. Logarithmic equations • Basic form: C logax = k. • Solve for logax. • Exponentiate each side with base a. This makes the logax side equal x because alogax= x • Solve.

  11. Try these log x + log (2x+1) = log 7 2log23x= 1

  12. 5.7 Objectives • Find an exponential model. • Find a logarithmic model.

  13. Types of models • Exponential • f(x) = Cax • Can be used to model data that increase or decrease rapidly over time • Logarithmic • f(x) = a + b logx • Can be used to model data that increase gradually over time • Logistic • f(x) = • Can be used to model data that at first increase slowly, then increase rapidly, and finally level of

  14. Exponential model f(x) = Cax

  15. Logarithmic model f(x) = a + b logx

  16. Logistic model

  17. assignment • Page 442-443 • 7-14 • 31-38 • Page 453 • 5-14 • 33-38 • Page 462 • 1-4

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