Using the Change-of-Base Rule in an ApplicationUse natural logarithms in the change-of-base rule and the function defined by
(given earlier) to estimate total crude oil imports (in millions of barrels) into the
United States in 2006. Compare this to the actual amount of 3685 million barrels. In
the equation, represents 1990.
For 2006,Change-of-base ruleUse a calculator.The model gives about 3586 million barrels for 2006, which is less than the actual
amount. NOW TRY
L 3586
= 2014 +384.7 a
ln 17
ln 2
b
ƒ 1172 = 2014 +384.7 log 2 17 x=17.
ƒ 1 x 2 = 2014 +384.7 log 2 x
x= 1
ƒ 1 x 2 = 2014 + 384.7 log 2 x
EXAMPLE 8
SECTION 10.5 Common and Natural Logarithms 609
NOW TRY
EXERCISE 8
Use the model in Example 8to
estimate total crude oil imports
into the United States in 2002.
Compare this to the actual
amount of 3336 million barrels.
NOW TRY ANSWER
- 3438 million barrels; This is
greater than the actual amount.
Complete solution available
on the Video Resources on DVD
10.5 EXERCISES
Concept Check Choose the correct response in Exercises 1–4.
1.What is the base in the expression?
A.e B. 1 C. 10 D.x
2.What is the base in the expression?
A.e B. 1 C. 10 D.x
3.Since and , between what two consecutive integers is the value of
log 6.3?
A.6 and 7 B.10 and 11 C.0 and 1 D. and 0
4.Since and , between what two consecutive integers is the value of
ln 6.3?
A.6 and 7 B.2 and 3 C.1 and 2 D.0 and 15.Concept Check Without using a calculator, give the value of.6.Concept Check Without using a calculator, give the value of.You will need a calculator for the remaining exercises in this set.Find each logarithm. Give approximations to four decimal places. See Examples 1 and 5.
7.log 43 8.log 98 9.log 328.4
10.log 457.2 11.log 0.0326 12.log 0.1741
- 15.ln 7.84
16.ln 8.32 17.ln 0.0556 18.ln 0.0217
19.ln 388.1 20.ln 942.6 21.
22.ln 1 7.46*e^32 23.ln 10 24.log e
- 15.ln 7.84
ln 1 8.59*e^22log 1 4.76* 1092 log 1 2.13* 1042ln e^23log 1031.6e^1 L2.718 e^2 L7.389- 1
100 = 1 101 = 10
ln xlog x