### Exam 4 - Chapter 6 and 7

- 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.
- 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.
- 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.
- 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.
- 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.
- Solve a non-linear system of equations. Look at problems 3 - 8 in the chapter 7 review.
- 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).
- 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.
- Solve a three by three system of linear equations. Look at problems in section 7.3. There are no missing terms.
- 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.
- 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.

- 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.