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

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Presentation transcript:

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

Solving Simple Equations Original Rewritten Solution Equation

Strategies for Solving Exponential and Logarithmic Equations 1. Rewrite the given equation in a form that allows the use of the One-to-One Properties of exponential or logarithmic functions. 2. Rewrite an exponential equation in logarithmic form and apply the Inverse Property of logarithmic functions. 3. Rewrite a logarithmic equation in exponential form and apply the Inverse Property of exponential functions.

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

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

Solve and approximate the result to three decimal places.

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

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

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

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.