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Solving Exponential and Logarithmic Equations

Learn how to solve exponential and logarithmic equations with clear examples and step-by-step instructions. Discover strategies for handling different scenarios and identifying extraneous solutions.

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Solving Exponential and Logarithmic Equations

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  1. Solving Exponential and Logarithmic Equations Section 6.6 beginning on page 334

  2. Solving Exponential Equations When both sides of an exponential equation have the same base, or can be re-written to have the same base, you can find the log of each side and solve the resulting equation. Example 1: a) b) We cant re-write these with the same base so we must find of each side. Taking the log of both sides allows you to set the exponents equal to each other.

  3. Solving Logarithmic Equations Example 3: a) b) Finding e to the power of each side allows us to set the values in the parenthesis equal to each other. Find 2 to the power of each side so we can undo the log. (This is called exponentiating ! :D )

  4. Solving Logarithmic Equations Example 4: Solve Use properties of logs to condense the logarithms . Then exponentiate both sides using 10 as the base. Solve the resulting equation. Since is undefined, is extraneous.

  5. This is what you should write down.

  6. Solving an Exponential Inequality Example 5: Solve Exact Solution: Approximate Solution:

  7. Solving a Logarithmic Inequality Example 6: Solve Since is only defined when so we have to write the solution as a compound inequality.

  8. Monitoring Progress Solve the equation. 1) 2) 3) Solve the equation. Check for extraneous solutions. 5) 6) 7) 8) Solve the inequality. 9) 10) 11) 12)

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