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5.4 Exponential and Logarithmic Equations

5.4 Exponential and Logarithmic Equations. Essential Questions: How do we solve exponential and logarithmic equations?. Solving Simple Equations. Original Rewritten Solution Equation Equation.

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5.4 Exponential and Logarithmic Equations

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  1. 5.4 Exponential and Logarithmic Equations Essential Questions: How do we solve exponential and logarithmic equations?

  2. Solving Simple Equations Original Rewritten Solution Equation Equation

  3. Strategies for Solving Exponential and Logarithmic Equations • Rewrite the given equation in a form that allows the use of the One-to-One Properties of exponential or logarithmic functions. • Rewrite an exponential equation in logarithmic form and apply the Inverse Property of logarithmic functions. • Rewrite a logarithmic equation in exponential form and apply the Inverse Property of exponential functions.

  4. Solution: a. Solving Exponential Equations • Solve each equation and approximate the result to three decimal places. a. b. b. Take natural log of each side. Use a calculator.

  5. Solution: Solving an Exponential Equation • Solve and approximate the result to three decimal places. Original equation. Subtract 5 from each side. Take natural log of each side. Inverse Property. Use a calculator.

  6. Solve and approximate the result to three decimal places.

  7. Solving a Logarithmic Equation a. Solve ln x = 2 b. Solve Solution: a. Exponentiate each side. b. Check this in the original equation.

  8. Solving a Logarithmic Equation • Solve and approximate the result to three decimal places. Solution: Exponentiate each side.

  9. Solving a Logarithmic Equation • Solve Solution: Exponentiate each side (base 5).

  10. Checking for Extraneous Solutions • Solve Solution: The solutions appear to be 5 and -4. However, when you check these in the original equation, only x = 5 works.

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