ALGEBRA II: CHAPTER 4 TEST REVIEW
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8) 8 2 = y
Graph the transformation: f(x) = -|x+2| -3
Evaluate the expression without using a calculator.
9) log8 512
1
10) log 3
9
11) log 108
12) ln
3
e
1)
Expand or condense
13) log 4 (16x)
Solve the problem.
2) The size of the coyote population at a
national park increases at the rate of 5.1%
per year. If the size of the current population
is 193, find how many coyotes there should
be in 4 years. Use the function
f(x) = 193e0.051t and round to the nearest
14) log2
3
whole number.
Use the compound interest formulas A = P 1 +
16
x-1
15) log 4
r nt
and
n
A = Pe rt to solve.
16)
3) Find the accumulated value of an
investment of $13,000 at 8% compounded
semiannually for 5 years.
7
q2 p
1
log7 x + log7 y
2
17) 4ln a - 3 ln b
4) Find the accumulated value of an
investment of $8000 at 9% compounded
continuously for 4 years.
18) 4 log7 3 +
1
1
log7 (r - 8) - log7 r
5
2
Use common logarithms or natural logarithms and a
calculator to evaluate to four decimal places
Write the equation in its equivalent exponential form.
19) log 0.8 14
5) log b 16 = 2
Solve the equation by expressing each side as a power
of the same base and then equating exponents.
20) 4 (3x - 7) = 16
6) log 6 216 = x
Write the equation in its equivalent logarithmic form.
7) 5 2 = x
1
21) ex + 8 =
1
e9
Solve the exponential equation. Express the solution set
in terms of natural logarithms.
+
22) 2 x 8 = 5
+
23) e x 7 = 4
24) 4 x + 4 = 5 2x + 5
Solve the exponential equation. Use a calculator to
obtain a decimal approximation, correct to two decimal
places, for the solution.
25) 6ex = 26
26) e3x - 5 - 1 = 1282
Solve the logarithmic equation. Be sure to reject any
value that is not in the domain of the original
logarithmic expressions. Give the exact answer.
27) log 2 (x - 3) = 3
28) log 5 (x - 2) = -2
29) ln x + 8 = 5
30) log2 (x + 3) - log2 (x + 1) = 2
31) log 3 (x + 6) + log 3 (x - 6) - log 3 x = 2
32) log 14 (x - 5) = 1 - log 14 x
33) log 3x = log 5 + log (x - 2)
34) ln (x - 6) + ln (x + 1) = ln (x - 15)
Solve the problem.
35) If Emery has $1000 to invest at 8% per year
compounded monthly, how long will it be
before he has $1800? If the compounding is
continuous, how long will it be? (Round
your answers to three decimal places.)
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