Before the invention of calculators, logarithms took much longer to evaluate. (Think of the older generations who went to college in the 1920s... The math they learned was the same, but was all done BY HAND). In the back of their textbooks, they had appendices that looked like this: Prime In(Prime) log(Prime) In(2) = 0.6931 log(2) = 0.3010 In(3) = 1.0986 log(3) = 0.4771 In(5) = 1.6094 log(5) = 0.6990 %3D 5. In(7) = 1.9460 log(7) = 0.8451 In(11) = 2.3979 | log(11) = 1.0414 %3D 11 %3D Using the fact that the number 679, 140 = 2 * 32 *5 * 7 *11 as its prime factorization: (a) use the properties of logs to expand In(679, 140) as far as possible Hint... expand In(22 * 32 *5 * 7° * 11) as far as possible (b) using the table above, plug in the values for each logarithm to four decimal places. What is your answer using the rounded values in the table? (c) Using your calculator, what is the value of In(679140) to 6 decimal places? Explain your answer and why it is similar/different than the answer in part (b) 3.

Before the invention of calculators, logarithms took much longer to evaluate. (Think of the older generations who went to college in the 1920s... The math they learned was the same, but was all done BY HAND). In the back of their textbooks, they had appendices that looked like this: Prime In(Prime) log(Prime) In(2) = 0.6931 log(2) = 0.3010 In(3) = 1.0986 log(3) = 0.4771 In(5) = 1.6094 log(5) = 0.6990 %3D 5. In(7) = 1.9460 log(7) = 0.8451 In(11) = 2.3979 | log(11) = 1.0414 %3D 11 %3D Using the fact that the number 679, 140 = 2 * 32 5 7 11 as its prime factorization: (a) use the properties of logs to expand In(679, 140) as far as possible Hint... expand In(22 32 5 7° * 11) as far as possible (b) using the table above, plug in the values for each logarithm to four decimal places. What is your answer using the rounded values in the table? (c) Using your calculator, what is the value of In(679140) to 6 decimal places? Explain your answer and why it is similar/different than the answer in part (b) 3.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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