Expert answer:I need help with a math problem
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math.docx
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1.
Suppose N is a positive integer such that log N ≈ 51.2. How many digits does N have?
A) 51
B) 52
C) 3
D) Cannot be determined
2. Suppose x is such that log8 x = 216.25 . Evaluate log8 29 x . Round your answer to three decimal places.
A) 245.25
B) 187.250
C) 7.457
D) 6,271.25
3. Evaluate log6 (64 xy) assuming that log6 x = 7.5 and log6 y = 8.9 .
4. Evaluate log9 x100 assuming that log3 x = 10.5 .
A) 1,050
B) 525
C) 60.5
D) 105.25
5. Find all numbers x that satisfy the equation log6 ( x + 8) − log6 ( x − 6) = 4 . Round your answer to two
decimal places.
6. Find an integer k such that 19k has 308 digits.
1
of the atoms in a sample decay after 6 years. How many
4
years is the half-life of this isotope? Round your answer to the nearest tenth.
7. Suppose a radioactive isotope is such that
8. A human bone is founded in your backyard. The ratio of carbon-14 to carbon-12 in the bone is 40% at
the corresponding ratio for living organisms. Calculate the age of the bone.
A) 5,250 years
B) 30,495 years
C) 7,575 years
D) 5,729 years
9. Suppose log a = 106.68 and log b = 109.68. Evaluate b/a.
10. Suppose log2 a = 1.27 and log2 b = 3.73. Evaluate ab.
A) 32
B) 16
C) 8
D) 64
11. Suppose you scream at 80 decibels and whisper at 30 decibels. What is the ratio of the sound intensity of
your scream to the sound intensity of your whisper? Give your answer as a power of 10.
12. How many times brighter is a star with apparent magnitude 6 than a star with apparent magnitude 21?
A) 10,000 times brighter
C)
1,000,000 times brighter
B)
D)
It is not brighter
1,000 times brighter
13. Two earthquakes were registered the same day in a small south Pacific island, the first one with Richter
magnitude 4.4 and the second one with Richter magnitude 3.9. Approximately how many times more
intense was the first earthquake than the second one? Round your answer to the nearest tenth.
14. Evaluate log2(8xy) assuming that log2x = 12.7 and log2y = 7.1.
x
15. Evaluate log 3 assuming that log3x = 12.3 and log3y = 7.9.
9y
1
16. Evaluate log 7
assuming that log 7 x = 3.7 and log 7 y = 4.1.
y
17. Suppose that you deposit into a savings account one dime on January 1, two dimes on January 2, four
dines on January 3, and so on, doubling the amount of your deposit each day. After how many days, will
your daily deposit exceed $100,000,000?
184
18. Without using a calculator or computer, give a rough estimate of 2 .
36
A) 10
36
B) 2 10
64
36
C) 2 10
36
D) 64 10
19. Suppose $3,200 is deposited in a bank CD account paying 6% interest per year, compounded 2 times per
year. How much will be in the CD account at the end of 16 years? Round your answer to the nearest
cent.
A) $20,650.84
B) $8,240.26
C) $8,129.13
D) $5,135.06
20. Suppose a bank wants to advertise that $2,000 deposited in its savings account will grow to $2060 in
one year. This bank compounds interest 4 times per year. What annual interest rate must the bank pay?
Round your answer to one decimal place.
21. Find a number t such that ln (3t – 4) = 3.
22. Find a number x such that e7 x −1 = 9 .
A)
ln(9) + 1
7
B)
ln(9) − 1
7
C)
ln(7) + 1
9
D)
23. Find all numbers x that satisfy the given equation.
ln(9 x)
=2
ln(10 x)
24. Find a number x such that e 2 x − 11e x = 12.
ln(7) − 1
9
25. Find a number y such that
2 + ln y
= 0.5.
5 + ln y
26. Assuming that f is a function defined by f(x) = 6 – 9ln(x).
A) Find the domain of f.
B) Find the range of f.
C) Find a formula for f -1.
27. Find all numbers x such that e2x + ex = 20. Round the answer to 4 decimal places.
28. What is the area of the region under the curve y =
and x = e11.
29. Find all numbers x such that ln( 2 − 3) = 4 .
1
, above the x-axis, and between the lines x = 1
x
…
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