math104
Katina4
week_6_quiz.docxWrite the equations in logarithmic form.
(a)
343 = 73
(b)
64 =
1
8
−2
(c)
a = bc
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Use the definition of logarithm to simplify each expression.
(a)
log10 10
(b)
log10 100
(c)
log10 10−2
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Solve each exponential equation. Give the exact value for x.
(a)
8x =
1
64
x =
(b)
5x = 8
x =
(c)
6x = 4.5
x =
(d)
3x = 4
x =
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Find a simplified value for x by inspection. Do not use a calculator.
(a)
log8 64 = x
x =
(b)
log2 8 = x
x =
(c)
log3 243 = x
x =
(d)
log4 64 = x
x =
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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 9 + ln 18
(b)
ln 3 − 2 ln(5 + 7)
(c)
ln 3 − 2(ln 4 + ln 8)
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A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of
5.5 cross product 102
µm. Find this earthquake's magnitude. (Round your answer to one decimal place.)
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Find the future value, using the future value formula and a calculator. (Round your answer to the nearest cent.)
$819 at 5.5% compounded quarterly for 3 years
$
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Suppose that an insurance agent offers you a policy that will provide you with a yearly income of $70,000 in 30 years. What is the comparable salary today, assuming an inflation rate of 5% compounded annually? (Round your answer to the nearest cent.)
$
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Convert the credit card rate to the APR.
Oregon,
1
1
4
%
per month
%
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Assume the car can be purchased for 0% down for 60 months (in lieu of rebate).
A car with a sticker price of $42,150 with factory and dealer rebates of $5,100
(a) Find the monthly payment if financed for 60 months at 0% APR. (Round your answer to the nearest cent.)
$
(b) Find the monthly payment if financed at 2.5% add-on interest for 60 months. (Round your answer to the nearest cent.)
$
(c) Use the APR approximation formula to find the APR for part (b). (Round your answer to one decimal place.)
%
(d) State whether the 0% APR or the 2.5% add-on rate should be preferred.
0% APR 2.5% add-on rate
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Use a calculator to evaluate an ordinary annuity formula
A = m
1 +
r
n
nt
− 1
r
n
for m, r, and t (respectively). Assume monthly payments. (Round your answer to the nearest cent.)
$150; 5%; 40 yr
A = $
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Find the monthly payment for the loan. (Round your answer to the nearest cent.)
$800 loan for 12 months at 11%
$
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