College Algebra 9th txtbk

360 CHAPTER 5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
display an ordered pair, representing a complex number, as the value of log (3.24), rather
than an error message. You should interpret such a display as indicating that the number
entered is not in the domain of the logarithmic function as we have defined it.]
MATCHED PROBLEM 6
Use a calculator to evaluate each to six decimal places.
(A) log 0.013 529 (B) ln 28.693 28 (C) ln (0.438)
When working with common and natural logarithms, we will follow the common practice
of using the equal sign “ ” where it might be technically correct to use the approximately
equal sign “ .” No harm is done as long as we keep in mind that in a statement such
as log 3.184 0.503, the number on the right is only assumed accurate to three decimal
places and is not exact.
ZZZ EXPLORE-DISCUSS 3
Graphs of the functions f (x) log x and g(x) ln x
are shown in the graphing calculator display of Figure
3. Which graph belongs to which function? It
appears from the display that one of the functions
might be a constant multiple of the other. Is that true?
Find and discuss the evidence for your answer.
0
2
5
2
Z Figure 3
EXAMPLE 7 Calculator Evaluation of Logarithms
Use a calculator to evaluate each expression to three decimal places.
log 2
(A) (B) log 2
log 1.1
1.1
(C) log 2 log 1.1
log 2
SOLUTIONS (A) Enter as
log 1.1 7.273
(B)
log 2
(log 2) (log 1.1).
Enter as
1.1 0.260
log (2 1.1).
(C) log 2 log 1.1 0.260. log 2
Note that log 2 log 1.1, but
log 2
log 1.1
(see Theorem 2).
1.1 log 2 log 1.1
MATCHED PROBLEM 7
Use a calculator to evaluate each to three decimal places.
ln 3
3
(A) (B) ln (C) ln 3 ln 1.08
ln 1.08 1.08
We now turn to the opposite problem: Given the logarithm of a number, find the number.
To solve this problem, we make direct use of the logarithmic–exponential relationships, and
change logarithmic expressions into exponential form.