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1. 2.5/2.5 points | Previous Answers
Write the equations in logarithmic form.
(a)
729 = 93
(b)
16 =
(c)
a = bc
1 −2
4
2. 2.5/2.5 points | Previous Answers
Use the definition of logarithm to simplify each expression.
(a)
log10 10
1
(b)
1 log10 1,000
3
3
(c)
log10 10−4
-4
-4
3. 1.86/2.5 points | Previous Answers
Solve each exponential equation. Give the exact value for x.
(a)
3x =
1
9
x=
(b)
7x = 10
x=
(c)
6x = 4.5
x=
(d)
x=
2x = 3
4. 2.5/2.5 points | Previous Answers
Find a simplified value for x by inspection. Do not use a calculator.
(a)
log4 16 = x
x= 2
(b)
2 log2 32 = x
x= 5
(c)
5 log3 243 = x
x= 5
(d)
x= 3
5 log4 64 = x
3
5. 2.5/2.5 points | Previous Answers
Contract the expressions. That is, use the properties of logarithms to write each expression as a single logarithm with a coefficient of 1.
(a)
ln 3 − 2 ln 5 + ln 10
(b)
ln 3 − 2 ln(8 + 4)
(c)
ln 3 − 2(ln 4 + ln 8)
6. 0/2.5 points | Previous Answers
A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of
4.2
5.5
102 µm. Find this earthquake's magnitude. (Round your answer to one decimal place.)
6.6
7. 0/2.5 points | Previous Answers
Find the present value, using the present value formula and a calculator. (Round your answer to the nearest cent.)
Achieve $225,500 at 8.55% compounded continuously for 8 years, 135 days.
$ 110242.21
110,244.09
8. 2.5/2.5 points | Previous Answers
Suppose that an insurance agent offers you a policy that will provide you with a yearly income of
$30,000 in 30 years. What is the comparable salary today, assuming an inflation rate of 6% compounded annually? (Round your answer to the nearest cent.)
$
