# Study Guide - Chapter 6

## Math 116

- Sketch the graph of an exponential and logarithmic function on the same coordinate system.
Look at problems 35 - 38 in section 6.2.
- Rewrite an exponential equation in logarithmic form (look at 31-32 in the review*) and a
logarithmic equation in exponential form. Two parts.
- Evaluate the given expression without a calculator. Actually, you can use a calculator, I just
want exact answers. Five parts. Look at problems 33 - 39 in the review* and problems 13 -
16 in section 6.4.
- Evaluate each logarithm using the change of base formula. Round answers to four decimal
places. Two parts. Look at problems 41 - 44 in the review* for one of the two parts.
- Use properties of logarithms to write the expression as the sum, difference, and/or multiple of
logarithms. Three parts. Look at problems 45 - 50 in the review*.
- Use properties of logarithms to write the expressions as the logarithm of a single quantity.
Three parts. Look at problems 51 - 56 in the review*.
- Approximate the logarithm using properties of logarithms and the approximations of key
logarithms given. Then find the base used. Three parts. Look at problems 61 - 64 in the
review. The logarithms are the same as in 61 - 64, but the base is different than what the book
used.
- Solve each equation. Round the answers to three decimal places. Five parts. Look at
problems 67 - 76 in the review*.
- Find the exponential function which passes through the given points. Look at problems 77 -
80 in the review.
- Application problem involving exponentials. Look at problems 19 - 22 in the review. Your
problem is to find the model, not evaluate it at a given time.
- Application problem involving logarithms. Look at problems 49 - 50 in section 6.5. Hint: The
percent change (increase or decrease) is the change (New-Old) divided by the Old times 100%.
A change from 50 to 60 is a (60-50)/50x100%=20% increase.
- Find a logistics curve. Look at problem 57 in section 1; 41, 42, 44 in section 5; 82 in the
chapter review. Your problem will be to find the model, not to evaluate it at certain times.

* means the problem is straight from the text.
Be sure to bring your calculator to the exam. Graphing calculators are allowed on this exam.

Problems 9 - 12 may be worked in groups of up to size 3.