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Mastering Exponential Equations with Logarithms

Learn to solve exponential equations using common logarithms and the change of base formula. Examples and exercises included.

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Mastering Exponential Equations with Logarithms

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  1. 6.6 – Solving Exponential Equations Using Common Logarithms. Objective: TSW solve exponential equations and use the change of base formula.

  2. Change of base formula: The change of base formula allows us to change any logarithm into base 10. logb x = log x log b Example: log8 12 =

  3. To evaluate logarithms - Use the change of base formula to evaluate logarithms which are not base 10. Examples: • log9 4 2. log8 3 3. 9 – log3 7

  4. Solving equations in exponential form: • Get the equation in the form “by = x” • Rewrite the exponential equation in logarithmic form (be sure you do not have any negative numbers within the logarithm) • Use the change of base formula to evaluate the logarithm. • Solve for x.

  5. Examples: • 2x = 49 2. 8x = 240

  6. Examples: 3. 2x+1 = 30 4. 67 –2-x = 39

  7. Examples: 5. 5x +12= 67 6. 15x^2 = 110

  8. Homework… pgs. 519-520 #’s 1-4(all), 6-8(all), 17-21(odds), 23-37(odds), 41-46(all)

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