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Exponential and Logarithmic Equations

Exponential and Logarithmic Equations. Lesson 5.6. y = 0.1 (10 x ). y = 0.5. Solving Exponential Equations Graphically. Given Graphical Solution Graph each side of the equation Use calculator to find intersection. Solving Exponential Equations Symbolically. Given

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Exponential and Logarithmic Equations

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  1. Exponential and Logarithmic Equations Lesson 5.6

  2. y = 0.1 (10x) y = 0.5 Solving Exponential Equations Graphically • Given • Graphical Solution • Graph each side of the equation • Use calculator to find intersection

  3. Solving Exponential Equations Symbolically • Given • Isolate the coefficientwith the exponent • Take log of bothsides • Use logarithm properties • Use division x

  4. Try It Out • Given 3(2 x – 2) = 99 • Part of class solve graphically • Part of class solve symbolically

  5. Logarithmic Equation • Consider ln 4x = 1.5 • Symbolic solution • Raise to the power of the base • Use property of logarithms • Use Division

  6. Logarithmic Equation • Graphical solution of ln 4x = 1.5 • As before graph both sides of the equation • y = ln 4x y = 1.5 • Use calculatorto find intersection

  7. Try It Out • Given • Part of class solve graphically • Part of class solve symbolically Will they ever meet again? Now what?

  8. Applications • Gambling revenues (in billions $) from 1991 to 1995 can be modeled by • x is the year, x = 0 is 1991 • When did revenues reach $45 billion?

  9. Assignment • Lesson 5.6 • Page 426 • Exercises 1 – 47 EOO and 51 – 67 odd

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