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Solving Exponential & Logarithmic Equations Graphically & Symbolically

Learn to solve exponential and logarithmic equations using graphical and symbolic methods. Use calculators and properties of logarithms for accurate solutions. Apply to practical scenarios and practice with provided exercises.

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Solving Exponential & Logarithmic Equations Graphically & Symbolically

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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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