Algebra II Workbook For Dummies by Mary Jane Sterling

Author:Mary Jane Sterling
Language: eng
Format: epub, pdf
ISBN: 9781119543121
Publisher: Wiley
Published: 2019-03-26T00:00:00+00:00

5log 9

45log 1

18 Determine which of the following is equivalent to .

19 Determine which of the following is equivalent to .

20 Determine which of the following is equivalent to ln e.

e

0

1

ee

21 Determine which of the following is equivalent to log6 1.

6

0

1

–6

22 Determine which of the following is equivalent to log 8.

log 42

3log 2

2log 3

4log 2

Presto-Chango: Expanding and Contracting Expressions with Log Functions

The logarithmic expression is pretty complicated with its numerator, denominator, radical, products, and powers. The beauty of logarithms is that the rules governing them allow you to pull apart and simplify these rather intricately constructed terms. For instance, using the rules of logarithms, you can write the above expression as . Yes, you have five separate terms now instead of the one, but each of the terms is much simpler — all the logarithms have arguments that are polynomials.

In other mathematics courses, such as calculus, you expand the logarithms in order to have an easier time when computing derivatives. Then, in a later study of math, you take the expanded format and change it back into a single logarithm. You can make all these spectacular changes using the laws of logarithms, which I cover earlier in this chapter, in the section “Checking out the Properties of Logarithms.”

Q. Show how to expand the logarithm to produce the answer given in the section intro.

A. First, use the rule for the log of a quotient to rewrite the logarithm as . Next, use the rule for the log of a product to split up the factors in the two terms. Be sure to distribute the negative sign over the two terms that come from the second term (the one after the minus sign):

.

Now change the 4 in the first term to a power of 2 and the radical to a fractional power:

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