Math 116: Chapter 4 Study Guide
- Match the exponential function with its graph. Look at problems 4.1.23 - 4.1.30*
- Match the logarithmic function with its graph. Look at problems 4.2.45 - 4.5.50*
- Match the function with its graph. Look at problems 4.5.1 - 4.5.6*
- Simplify the expressions without the use of a calculator. Look at problems 4.3.67 - 4.3.79,
4.4.21 - 4.4.25
- 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.
- Write the expression as the logarithm of a single quantity. Three parts. Look at problems
4.3.41 - 4.3.54.
- 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.
- Evaluate a logarithm using the change of base formula. Look at problems 4.3.11 - 4.3.18.
- 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 logb 2 = 0.7565 and logb 3 = 1.1990, then the logb 6 = logb (2*3) = logb 2 +
logb 3 = 0.7565 + 1.1990 = 1.9555. To find the base, rewrite in exponential form ( b0.7565 = 2)
and then take the inverse power of both sides (b = 2(1/0.7565) = 2.50)
- 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
- 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.
- pH problem. Be able to convert pH into the concentration of hydrogen ions. Two parts.
Look at problems 4.5.63 - 4.5.66.
- Find the exponential model. Look at problems 4.5.43 - 4.5.47.
- 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.