Download Test 3 Logarithmic Properties and Equations REVIEW

Test 3 Logarithmic Properties and Equations REVIEW
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
1) At what interest rate must $4600 be compounded annually to equal $9107.69 after 14 yr?
(Round to the nearest percent.)
2) What is the rate on an investment that triples $1599 in 27 years? Assume interest is
compounded monthly.
1)
2)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
3) Suppose f(x) = 29.9 + 1.4log (x + 1) models salinity of ocean water to depths of 1000 meters at a
certain latitude. x is the depth in meters and f(x) is in grams of salt per kilogram of seawater.
Approximate the depth (to the nearest tenth of a meter) where the salinity equals 31.
A) 5.1 m
B) -0.8 m
C) 7.1 m
D) -0.9 m
3)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
4) How long will it take for $1700 to grow to $11,800 at an interest rate of 5.2% if the interest is
compounded quarterly? Round the number of years to the nearest hundredth.
4)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
5) Suppose that y =
2 - log (100 - x)
can be used to calculate the number of years y for x percent of a
0.25
5)
population of 910 web-footed sparrows to die. Approximate the percentage (to the nearest whole
per cent) of web-footed sparrows that died after 3 yr.
A) 82%
B) 76%
C) 84%
D) 80%
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the equation and express the solution in exact form.
6) ln ex - ln e8 = ln e2
6)
7) ln(4x - 5) + ln (x - 5) = ln 25
7)
8) log5 (x + 8) + log5 (x - 8) = 3
8)
Write as the sum and/or difference of logarithms. Express powers as factors.
7 5
p q
9) log
6
t2
9)
Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers.
10) (loga q - loga r) + 5 loga p
10)
1
Write the expression in condensed form.
11) 5 log a m - log a n
11)
Write the expression in expanded form.
x3 z
12) log
y2
13) loga
x4
12)
3
x+5
(x -2)2
13)
Solve the logarithmic equation.
14) log (x + 10) - log (x + 4) = log x
14)
15) log2 (x + 4) + log2 (x - 4) = 1
15)
16) ln(3x - 1) = ln 2 - ln (x - 2)
16)
17) log (x + 3) = 1 - log x
17)
Solve the equation.
18) log3 x + log3 (x - 24) = 4
18)
19) log2 (3x - 2) - log2 (x - 5) = 4
19)
20) log
20)
10
(x + 30) = 3 - log
10
x
2
Answer Key
Testname: TEST 3 05112017 REVIEW
1)
2)
3)
4)
5)
6)
5%
4.1%
A
37.50 yr
A
{10}
25
7)
4
8) {3 21}
1
1
9) log p + log q - 2 log t
6
6
6
7
5
10) loga
qp5
r
11) log a
m5
n
12) 3 log x + log z - 2 log y
1
13) 4 loga x + loga (x + 5) - 2 loga (x - 2)
3
14) 2
15) 3 2
7
16)
3
17)
18)
19)
20)
2
{27}
{6}
{20}
3