Section 10.4: Review for Chapter 10

Studying for a chapter examination is a personal process, one which nobody else
can do for you. Simply take the time to review what you have done.

Here are the new terms in Chapter 10.

Addition law of logarithms [10.2}
Argument [10.1}
Change of base theorem [10.3}
Common logarithm [10.1}
Decay formula [10.3}
Decibel [10.3}
Evaluate [10.1}
Exact solution [10.1}
Exponential [10.1}
Exponential equation [10.1}
Grant’s tomb properties [10.2}
Growth formula [10.3}
Half-life [10.3}
Laws of logarithms [10.2}
Log of both sides theorem [10.2}
Logarithm [10.1}
Logarithmic equation [10.2}
Logarithmic scale [10.3}
Micrometer [10.1; 10.3}
Multiplicative law of logarithms [10.2}
Natural logarithm [10.1}
Richter number [10.3}
Richter scale [10.3}
Subtractive law of logarithms [10.2}

If you can describe the term, read on to the next one; if you cannot, then look it up in the text (the section number is shown in brackets).


Can you explain each of these important ideas in your own words?

A logarithm is an exponent. That is, log (base b) A is the exponent on a base that gives the result A. [10.1}
Change of base theorem [10.1}
Fundamental properties of logarithms [10.2}
Log of both sides theorem [10.2}
Laws of logarithms — additive, subtractive, and multiplicative laws [10.2}

Next, make sure you understand the types of problems in Chapter 10.


Know the definition of a logarithm. [10.1}
Evaluate logarithms. [10.2}
Use the Grant’s tomb properties to simplify logarithmic expressions. [10.1, 10.2}
Solve exponential equations. [10.1}
Solve logarithmic equations. [10.2}
Solve applied problems of growth and decay. [10.3}

Once again, see if you can verbalize (to yourself) how to do each of the listed types of problems. Work all of Chapter 10 Review Questions (whether they are assigned or not).

Work through all of the problems before looking at the answers, and then correct each of the problems. The entire solution is shown in the answer section at the back of the text. If you worked the problem correctly, move on to the next problem, but if you did not work it correctly (or you did not know what to do), look back in the chapter to study the procedure, or ask your instructor. Finally, go back over the homework problems you have been assigned. If you worked a problem correctly, move on the next problem, but if you missed it on your homework, then you should look back in the text or talk to your instructor about how to work the problem. If you follow these steps, you should be successful with your review of this chapter.

We give all of the answers to the Chapter Review questions (not just the odd-numbered questions), so be sure to check your work with the answers as you prepare for an examination.