eday Lessons HSCC Precalculus Logarithims F-LE 4, BF-B 5 11/2014 E-Lesson 1

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1 eday Lessons HSCC Precalculus Logarithims F-LE 4, BF-B 5 11/2014 E-Lesson 1

2 Enclosed are the E-Day assignments required to make up the 3 calamity days missed during the school year for High School Common Core. Failure to complete the assignments will result in your being marked absent for the 3 calamity days. While you are completing the assignments remember to: 1. Read the questions carefully and make sure you answer the question that is asked. 2. Show all work for each problem on a separate sheet if needed. 3. Check your work when you are finished. Due Date: Precalculus Logarithims F-LE 4, BF-B 5 11/2014 E-Lesson 1

3 Name Date Per Properties of Logarithms Part I: 1. Evaluate log 28 + log Think of a logarithm expression with base 2 whose value is the same as the value in #1. 3. Evaluate log 33 + log Think of a logarithm expression with base 3 whose value is the same as the value in #3. 5. Evaluate log1 + log Think of a common logarithm expression whose value is the same as the value in #5. 7. What pattern do you see in the problems above? How can you write log bu + log bv as a single logarithm? Part II: 8. Evaluate log 264 log Think of a logarithm expression with base 2 whose value is the same as the value in # Evaluate log 381 log 327. Precalculus Logarithims F-LE 4, BF-B 5 11/2014 E-Lesson 1

4 11. Think of a logarithm expression with base 3 whose value is the same as the value in # Evaluate log10,000 log Think of a common logarithm expression whose value is the same as the value in # What pattern do you see in the problems above? How can you write log bu log bv as a single logarithm? Part III: 15. Evaluate log Think of a logarithm expression with base 2 (besides log 264) whose value is the same as the value in # Evaluate log Think of a logarithm expression with base 3 (besides log 3729) whose value is the same as the value in # Evaluate log Think of a common logarithm expression (besides log10,000) whose value is the same as the value in # What pattern do you see in the problems above? How else can you write logbu k? Precalculus Logarithims F-LE 4, BF-B 5 11/2014 E-Lesson 1

5 Name Date Per Exercises with Logarithms 1. Which numbers x satisfy the equation: (log 3x)(log x5) = log 35? 2. Suppose that the Canadian dollar loses 5% of its value each year. How many years are needed in order that the Canadian dollar to lose 90% of its value? (That is, the future value of the dollar to become the present value of a dime.) 3. Simplify the product: P = (log 23)(log 34)(log 45)... (log 3132) 2 logb (loga a ) 4. If p = find a p. log a b 5. If log b (xy) = 11 and log b (x/y) = 5, what is log b x? Logarithms F-LE 4, BF-B 5 04/2014 E-Lesson 2-3

6 6. Positive integers A, B, and C, with no common factor greater than 1, exist such that A log B log = C. What is A + B + C? log What is the value of 25? 8. A computer manufacturer finds that when x millions of dollars are spent on research, the profit, P(x), in millions of dollars, is given by P( x) 20 5log x 3 to make a profit of 40 million dollars?. How much should be spent on research 3 9. Solve the system of equations y log2 2x and y log4 x for all x. 10. Solve the equation log 3 (x - 2) + log 3 10 = log 3 (x 2 + 3x 10) 11. log 2 (9-2 x ) = 3 x Logarithms F-LE 4, BF-B 5 04/2014 E-Lesson 2-3

7 Exponent, Log, & Logistic Fctn - C Name Date Per Why Settle for Time Estimation When You Can Be Exact? Luckily, logarithms allow us to solve for the t-variable in the compound interest formula. Let s see how we can use this fact to find out how long it takes any amount of money to double, triple, etc. 1. Rewrite the compound interest formula with the appropriate substitutions to indicate 11% interest, $100 to start, and annual compounding. Don t forget to substitute the correct value for A also (how much should it be if we re doubling our investment?). What does the formula now look like? 2. Solve this formula for t. See how this compares with your approximation in exercise 3a of the last activity. 3. Now create and solve an appropriate equation to represent tripling of our investment. Logarithms F-LE 4, BF-B 5 04/2014 E-Lesson 2-3

8 Exponent, Log, & Logistic Fctn - C 4. Do the same for quadrupling. 5. How long, in exact terms, should it take to multiply our initial investment by 10? 6. Observe the relationship between each problem above and the exact answer (in terms of logarithms). Without going through all the steps of solving an exponential equation, how long should it take our investment to double if the interest rate were 8%? How should our numerical answer compare with number 2 above? Be sure to justify your answers. Logarithms F-LE 4, BF-B 5 04/2014 E-Lesson 2-3