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Solving Exponential Equations: Step-by-Step Guide and Practice Assignments

This resource provides a thorough overview of solving exponential equations. Key steps include isolating the variable exponent, taking the logarithm of both sides, and utilizing logarithmic properties to find solutions. It covers practical examples such as solving equations like (5^x = 358) and provides problems for practice. The material also highlights essential skills needed for quizzes and homework assignments. Prepare effectively for your upcoming quiz on January 10 with exercises from page 331 and more.

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Solving Exponential Equations: Step-by-Step Guide and Practice Assignments

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  1. Today in precalculus • Go over homework • Notes: Solving Exponential Equations • Homework

  2. Steps to SolvingExponential Equations • Isolate the term with the variable exponent using algebra. • Take the log of both sides (or convert to a log equation) • Use properties of logs • Solve for the unknown.

  3. Example 5x = 358 log5x =log358 xlog5=log358 x = 3.654

  4. Example 3ex - 6 = 48 3ex = 54 ex = 18 lnex= ln18 x=ln18 x = 2.890

  5. Practice

  6. x = -1.839

  7. 2. 6e2x + 10 = 46 6e2x = 36 e2x = 6 2x = ln6 x = .896

  8. 3. 10e-x + 45 = 83 10e-x = 38 e-x = 3.8 -x = ln3.8 -x = 1.335 x = -1.335

  9. ex + 2e-x = 3 ex + 2e-x – 3 = 0 ex(ex + 2e-x – 3 = 0) e2x – 3ex + 2e0 = 0 e2x – 3ex + 2= 0 (ex – 2)(ex – 1) = 0 ex = 1 ex = 2 x = ln1 x = ln2 x = 0, .693

  10. ex – e-x = 10 ex – e-x – 10 = 0 ex(ex– e-x – 10 = 0) e2x – 10ex – e0 = 0 e2x – 10ex– 1 = 0 ex = 10.099 ex = -.099 x = ln10.099 x = ln(-0.099) x = 2.312

  11. Homework • Page 331: 1-6, 11-16, 29-33 • Quiz Friday, January 10

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