### Exam 4 - Chapter 6 and 7

1. Evaluate without using a calculator. There are two logarithmic expressions and two exponential expressions. Study the inverse properties in section 6.4. (Know them forwards and backwards). Four parts.
2. Use properties of logarithms to write the expression as a sum, difference, and or multiple of logarithms. Look at problems 45 - 50 in the chapter 6 review. Three parts.
3. Use properties of logarithms to rewrite the expression as the logarithm of a single quantity. Look at problems 51 - 56 in the chapter 6 review. Three parts.
4. Approximate the logarithm use the properties of the logarithms and the values given. Look at problems 61 - 64 in the chapter 6 review. Three parts. This isn't mentioned on the exam, but I will give you extra credit if you calculate the base used. Just write the base as part d to the problem. It will be up to you to remember this. I will disavow any knowledge of it in class - it is for those who bother grabbing the study guide off the Internet.
5. Solve for x, leave your answers in exact forms. Look at problems 67 - 76 in the chapter 6 review, except leave your answers in exact form. Four parts.
6. Solve a non-linear system of equations. Look at problems 3 - 8 in the chapter 7 review.
7. Solve a linear system of equations with two variables and two equations. Look at problems 11 - 18 in the chapter 7 review (except you don't have to use elimination).
8. Solve a system of equations with more variables than equations. Give answer in parametric form. Look at problems 29 in the chapter 7 review and 15 - 18 in section 7.3.
9. Solve a three by three system of linear equations. Look at problems in section 7.3. There are no missing terms.
10. Sketch the graph of the solution to a system of linear inequalities (like in linear programming). Look at problems 39 - 42 in the chapter 7 review.
11. Identify each statement as true or false. Five parts. These are general questions about material out of chapters 6 and 7.
Specifically, know the following.
• The log of a product is the sum of the logs.
• The log of a quotient is the difference of the logs.
• The conversion between exponential and logarithmic form.
• The domain of the exponential and logarithmic functions.
• The definitions of independent, dependent, consistent, and inconsistent systems.
12. Set up - do not solve - a system of equations which could be used to find the equation of a parabola which opens up or down and passes through the three given points. Look at problems 31 - 32 in the chapter 7 review.