Math 116: Chapter 4 Study Guide

1. Match the exponential function with its graph. Look at problems 4.1.23 - 4.1.30*
2. Match the logarithmic function with its graph. Look at problems 4.2.45 - 4.5.50*
3. Match the function with its graph. Look at problems 4.5.1 - 4.5.6*
4. Simplify the expressions without the use of a calculator. Look at problems 4.3.67 - 4.3.79, 4.4.21 - 4.4.25
5. Write the expression as a sum, difference, and/or constant multiple of logarithms and simplify (if possible). Three parts. Look at problems 4.3.19 - 4.3.38.
6. Write the expression as the logarithm of a single quantity. Three parts. Look at problems 4.3.41 - 4.3.54.
7. Solve the exponential and logarithmic equations. Give an exact answer. The problems have been designed so the answers can be found without a calculator. Five parts. Look at problems 4.4.27 - 4.4.33, 4.4.39 - 4.4.49, 4.4.55 - 4.4.59, 4.4.65 - 4.4.75.
8. Evaluate a logarithm using the change of base formula. Look at problems 4.3.11 - 4.3.18.
9. Use the table of logarithms to approximate other logarithms. The base will be unknown, so you won't be able to use the change of base formula to double-check your answer (until you answer part c, that is). Three parts. Find the base of the logarithm used in the table. Example: if the log_b 2 = 0.7565 and log_b 3 = 1.1990, then the log_b 6 = log_b (2*3) = log_b 2 + log_b 3 = 0.7565 + 1.1990 = 1.9555. To find the base, rewrite in exponential form ( b^0.7565 = 2) and then take the inverse power of both sides (b = 2^(1/0.7565) = 2.50)
10. Use your calculator to approximate the expression. Four parts. Look at problems 4.1.1 - 4.1.10 and 4.2.31 - 4.2.40. Be able to work with the limit definition of e - example 5 on page 320.
11. Express each melodic statement symbolically using variables. Classify each statement as true or false. An example of what I'm looking for is "The log of a product is the sum of the logs" could be written as "log xy = log x + log y" and it is true. Five parts.
12. pH problem. Be able to convert pH into the concentration of hydrogen ions. Two parts. Look at problems 4.5.63 - 4.5.66.
13. Find the exponential model. Look at problems 4.5.43 - 4.5.47.

Notes:

• There is none of 4.6 on the in-class test. There will be a take-home portion of the exam over section 4.6. The take-home portion is worth 15 points and is due the class period after the in-class portion.
• *'d problems are directly from the textbook.
• Problems 1-7 are designed to be done without the graphing calculator. If you use the graphing calculator on those problems, you may not have enough time to finish the exam.