Math 116: Chapter 4 Study Guide

1. Solve the exponential equation for x. Two parts. Look at problems 4.4.15-23
2. Solve the logarithmic equation for x. Two parts. Look at problems 4.4.28-36
3. Rewrite the exponential expression in logarithmic form. Look at problems 4.2.9-18
4. Rewrite the logarithmic expression in exponential form. Look at problems 4.2.1-8
5. Match the exponential function with its graph. Eight parts. Look at problems 4.1.15-22
6. Match the logarithmic function with its graph. Eight parts. Look at problems 4.2.47-52
7. Write the expression as a sum, difference, and/or constant multiple of logarithms and simplify (if possible). Three parts. Look at problems 4.3.27-46
8. Match the function with its graph. Twelve parts. Look at problems 4.5.1-6
9. Simplify the expressions without the use of a calculator. Thirteen parts. Look at problems 4.3.73-86, 4.4.37-42
10. Find the greatest integer of a logarithmic expression. In English, that means to give the first digit of a logarithm. For example, the log _5.4 412 is somewhere between 3 and 4 because 5.4³<412<5.4⁴. The greatest integer of any value between 3 and 4 is 3, so the answer is 3. The greatest integer function is symbolized using the double bracket. See page 111 for a discussion of the greatest integer function.
11. Write the expression as the logarithm of a single quantity. Three parts. Look at problems 4.3.49-68
12. Solve the equations. Give an exact answer. The problems have been designed so the answers can be found without a calculator. Pay attention to domain. Two parts. Look at problems 4.4.43-56
13. Solve the equations. Give an exact answer. The problems have been designed so the answers can be found without a calculator. Pay attention to domain. Three parts. Look at problems 4.4.89-96
14. Make a sign chart (like we did in chapter 3) to find the domain of a logarithmic function. Remember that a logarithm is only defined when its argument is positive.
15. Rewrite a logarithm using the change of base formula. Do not simplify, just rewrite.

Notes:

• No calculators allowed on the in-class portion of the exam.
• None of the problems on the test are straight from the text, but should be similar to the problems in the text.
• There is none of section 4.5 on the in-class test except for the matching.
• There is a take-home portion of the exam worth 30 points and is due the class period after the in-class portion.