# OSU MTH 111 - Act-#18 Exp & Log Eqns-Key (4 pages)

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## Act-#18 Exp & Log Eqns-Key

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- Pages:
- 4
- School:
- Oregon State University
- Course:
- Mth 111 - College Algebra

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Math 111 Name KEY Grp Exp Logarithmic Functions Equations and Models GrpAct 18 Sect 5 6 We have been talking about exponential and logarithmic functions for the past two weeks This activity combines those topics Exponential and logarithmic functions are incredibly powerful in modeling phenomena and you ll get to see some of those examples here 1 Warm Up Evalute the following logarithms without using a calculator If the logarithm is undefined write Undefined a log 3 1 0 b 1 log 2 3 8 c ln 1 Undefined d ln e15 15 e log 7 0 Undefined Change of Base Formula Let x a and b be positive real 2 Your calculator has a dedicated button for the natural logarithm and the common logarithm ln and log To compute logarithms of a different base using a calculator we can first use the change of base formula to convert to log or ln Use the change of base formula to compute each of the following logarithms using a calculator a log 7 0 91 numbers with Then Complete the following with the natural log ln 0 91 0 0485 ln 7 Complete with the common log b log 13 45 log 45 1 4841 log 13 To use a calculator we convert logarithms to ln or log using the change of base formula above 3 Solve each of the following equations Give exact and approximate solutions If no solution exists write No Solution a 9 5e0 05x 19 1 x ln 2 20ln 2 13 8629 0 05 b 3 2 x 2 99 x 2 ln 33 7 0444 ln 2 c log3 1 x 1 x 2 d 2x 4 x No Solution e 2x 1 x 0 Need a hint for how to get started on these You can either think about applying the inverse of the exponential function or you can think about rewriting the exponential equation as a log equation 4 The half life of carbon 14 is 5700 years A sample of carbon 14 originally contained 75 grams Let A t be the amount of carbon 14 left in the sample after t years a Give two ordered pairs t A t for this situation Explain what they represent in context 0 75 5700 37 5 b The amount of carbon 14 in the sample decays exponentially over time Give an exponential decay model for this in the form

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