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Honors Algebra 2
Chapter 8 Review
Name ____________________
Date _________ Hour _______
Graph each equation. State the domain and range.
1.
f(x) = 3(4)x – 6
2.
f(x) = 4x + 1 – 5
Solve each equation or inequality without using logarithms.
1
16x 
4.
5.
34x = 93x+7
64
x 2
1
 
 81 
3.
f(x) = 3(2/5)x-3 – 6
6.
43x = 32x-1
x2
27 ≤ 9
2x-1
9.
2x  2
1
 
 81 
x 4
7.
9
10.
A bacteria population started with 5000 bacteria. After 8 hours there were 28,000 in the sample.
a)
Write an exponential equation that could be used to model the number of bacteria after x
hours if the number of bacteria changes at the same rate.
b)
8.
3x
27
How many bacteria can be expected in the sample after 32 hours?
Write each equation in logarithmic form.
11.
25 = 32
12.
4-1/2 = ½
13.
e-1 = 1/e
14.
(0.5) -3 = 8
Write each equation in exponential form.
15.
log4 2 = 0.5 16.
ln 1 = 0
17.
log1/9 27 = -3/2
18.
log8 16 = 4/3
Evaluate each logarithm. Yup, show that work to find an EXACT answer.
19.
log27 3
20.
ln e-2
21.
log2 1/64
22.
log6 36
23.
26.
log8 32
log4 1
24.
log3/2 9/4
25.
log9 27
Solve each equation or inequality.
3
log16 x 
27.
2
28.
log 2
1
x
16
29.
log x 64 
31.
log5 x  3
32.
log 2 x  5
Use log5 2 ≈ 0.4307 to approximate the value of each expression.
33.
log5 1/8
34.
log5 10
35.
log5 2/5
Solve each equation. Check your solution.
36.
log5 (a+3) – log5 (a–1) = 1 37.
2log4 (x+3) = 6
38.
log2 (x+1) = 3 + log2 (x-6)
39.
41.
log4 n + log4 (n-4) = log4 5
30.
log 4 x  3
log5 x - log5 2 = log5 15
40. 2log3 x + log3 3 = log3 36
2
3
Put each equation or inequality into calculator ready form. Then solve, round to the nearest ten-thousandth.
42.
3x = 15
43.
8x+1 = 30
44.
12x-1 = 7x
45.
4ex – 11 = 17
46.
2e-x + 1 = 15
47.
2 + ex > 5
48.
35x > 24
49.
5x+2 ≤ 3x
50.
e-x > 18
Use the change of base formula to evaluate each logarithm. Round your answer to the nearest hundredth.
And yes, show the expression in calculator-ready form before you hit the buttons.
51.
log9 42
52.
log1/6 3
53.
log3 0.7
54.
You deposit $1000 into an account that pays an annual interest rate of 5% compounded quarterly.
nt
r

How long will it take for your money to double? Use A  P 1   .
 n
55.
If you deposit $2000 in an account paying 6.4% interest compounded continuously, how long will it
take for your money to triple? Use A = Pert
56.
Abe bought a car for $2500 that is expected to depreciate at a rate of 25% per year. What will be
the value of the car in 3 years?
57.
For a certain strain of bacteria, K is 0.72 when t is measured in days. Using the formula
y = aekt, how long will it take 10 bacteria to increase to 675 bacteria?
58.
The population of a city 20 years ago was 24,330. Since then, the population has increased at a
steady rate each year. If the population is currently 55,250, find the annual rate of growth for the
city.