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