Study Guide - Chapter 6

Math 116

  1. Sketch the graph of an exponential and logarithmic function on the same coordinate system. Look at problems 35 - 38 in section 6.2.
  2. Rewrite an exponential equation in logarithmic form (look at 31-32 in the review*) and a logarithmic equation in exponential form. Two parts.
  3. Evaluate the given expression without a calculator. Actually, you can use a calculator, I just want exact answers. Five parts. Look at problems 33 - 39 in the review* and problems 13 - 16 in section 6.4.
  4. Evaluate each logarithm using the change of base formula. Round answers to four decimal places. Two parts. Look at problems 41 - 44 in the review* for one of the two parts.
  5. Use properties of logarithms to write the expression as the sum, difference, and/or multiple of logarithms. Three parts. Look at problems 45 - 50 in the review*.
  6. Use properties of logarithms to write the expressions as the logarithm of a single quantity. Three parts. Look at problems 51 - 56 in the review*.
  7. Approximate the logarithm using properties of logarithms and the approximations of key logarithms given. Then find the base used. Three parts. Look at problems 61 - 64 in the review. The logarithms are the same as in 61 - 64, but the base is different than what the book used.
  8. Solve each equation. Round the answers to three decimal places. Five parts. Look at problems 67 - 76 in the review*.
  9. Find the exponential function which passes through the given points. Look at problems 77 - 80 in the review.
  10. Application problem involving exponentials. Look at problems 19 - 22 in the review. Your problem is to find the model, not evaluate it at a given time.
  11. Application problem involving logarithms. Look at problems 49 - 50 in section 6.5. Hint: The percent change (increase or decrease) is the change (New-Old) divided by the Old times 100%. A change from 50 to 60 is a (60-50)/50x100%=20% increase.
  12. Find a logistics curve. Look at problem 57 in section 1; 41, 42, 44 in section 5; 82 in the chapter review. Your problem will be to find the model, not to evaluate it at certain times.
* means the problem is straight from the text.

Be sure to bring your calculator to the exam. Graphing calculators are allowed on this exam.

Problems 9 - 12 may be worked in groups of up to size 3.