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Exponential & Logarithmic Equations: Solving and Applications

Learn how to solve exponential and logarithmic equations and apply them to real-world scenarios. Understand logarithmic equations with clear examples and solutions. Dive into earthquake energy calculations.

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Exponential & Logarithmic Equations: Solving and Applications

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  1. Exponential and Logarithmic Equations and Inequalities Essential Questions • How do we solve exponential and logarithmic equations and equalities? • How do we solve problems involving exponential and logarithmic equations? Holt McDougal Algebra 2 Holt Algebra 2

  2. A logarithmic equation is an equation with a logarithmic expression that contains a variable. There are two kinds of logarithmic equations: • Equations with logarithms on both sides of the equal sign. • Equations with logarithms only on one side. (exponentiate the equation) Check answer to make sure it does not give a log(x< 0).

  3. Solving Logarithmic Equations Solve the equation.

  4. Solving Logarithmic Equations Solve the equation.

  5. Solving Logarithmic Equations Solve the equation.

  6. Solving Logarithmic Equations Solve the equation.

  7. Solving Logarithmic Equations Solve the equation.

  8. Solving Logarithmic Equations Solve the equation.

  9. Solving Logarithmic Equations Solve the equation.

  10. Solving Logarithmic Equations Solve the equation.

  11. Solving Logarithmic Equations Solve the equation.

  12. Economics Application The moment magnitude M of an earthquake that releases energy E (in ergs) can be modeled by this equation: On October 9, 1984, the largest earthquake in Georgia occurred in Dalton with a magnitude of 4.2. How much energy did this earthquake release? 4.2 = 0.219ln E +1.17 Substitute 4.2 for M. Solve for E. The earthquake released about 1,020,309 ergs of energy.

  13. Lesson 9.2 Practice B

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