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Getting Started with Algebra 2 Changing Bases Name ____________________________ Class ____________________________ ID: 9842 In this activity, you will explore: Change-of-base formula Open the file Alg2Act2_ChangeBase_EN.tns on your handheld and follow along with your teacher to work through the activity. Use this document as a reference and to record your answers. Many calculators can only compute common logarithms (base 10) and natural logarithms (base e). While these two logarithms are the ones most frequently used, sometimes you might need to evaluate logarithms of other bases. To do this, the change of base formula is used. To discover this formula, some exploration is required. Evaluate the following using your TI-Nspire handheld. (Note: The templates for Exercises 1–3 have already been entered into the TI-Nspire handheld and may be found on pages 1.2–1.4.) 1. log7 5 2. log3 7 log12 5 3. log10 5 log10 7 4. log2 10 log5 10 5. log 5 log 7 6. Which of the expressions in Exercises 1–5 share the same value? What do these expressions have in common? 7. Based on your answer to Exercise 6, match each expression in Column A with an equivalent expression in Column B. Then confirm your answers using your handheld. Column A a. log3 2 b. 8. Rewrite the expression loga x as the quotient of two logarithms. log5.2 7 log5.2 3 c. log2 3 d. loge 2 loge 7 Column B log3 3 e. log3 2 f. log7 2 g. log3 2 log3 3 h. log3 7 ________________________________________ ©2008 Texas Instruments Incorporated Page 1 Getting Started with Algebra 2 9. The expression used in Exercise 8 is called the change of base formula. Why would we need to know the change of base formula? Give an example of when we would use the change of base formula. ____________________________________________________________________________ 10. Beginning with the Change of Base formula (the whole equality), prove that this relationship holds true for all numbers. Show all work below. (Hint: start with log a x m and convert to exponential form.) ©2008 Texas Instruments Incorporated Page 2