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Advanced Algebra Chapter 8 Review
Non-Calculator Part
Rewrite exponential functions as logarithmic and vice versa.
3
1) 53  125
2)
3) ln x  6
16 4  8
5)
ex  7
6)
log9
7) e5  x
1
 2
81
4)
log7 1  0
8)
ln 8  x
Write the expression as a sum or difference of logarithms or multiples of logarithms.
9)
10)
2
3
xy5
log 6 5x
y
ln
Write the expression as a single logarithm.
11)
1
2 ln y 
3
z3
12) 2log 2 x  3log 2 b  log 2 y  4log 2 a
ln x
Evaluate without a calculator.
13) log 2 32
14) log 64
6
15)
Solve each equation. Check your solutions.
17) 34x 1  32x  9
18) 1
25
 5x  6
log 3
1
27
16)
log 64 8
19) 82x  5  164x 1
20)
5y  3
9
 1 
 
 27 

y
21)
log b
22)
1
 3
64
23) log 2b2 1  log  6  9b 
6
6

24) log x 2  7  log  x  5
12
12
25)
1
log 9 8
3
26) log 2  log  y  4   log 6
3
3
3
log9 x 

log a 32 
5
2

27) log3 x  log3 x  log3 2  log3 18
28) 3log5 x  log5 2  log5 32
29)
1
log 2  2x 1  log 2 16  log 2  x  3
2
30) log  x  2   log  x  4   2
4
4
31)
1
1
log9 a  log9 64  log9 121
3
2
32) log  y  2   log  y  2   1
2
2
Graph each exponential or logarithmic function. State the domain and range of each. Describe any
transformations.
33) f (x)  2x 3
34) f  x   2x  3
35) f (x)  log  x  2 
3
36) f  x    log3 x  2
Calculator Part
Solve the following equations. Round to the nearest ten-thousandth.
37) ln 2x  7
38) 2e x  3  7
Evaluate each expression to the nearest ten-thousandth.
39) log 3.6
40) log 6 17
Solve the equations. Round to the nearest ten-thousandth
41) 2x  27
42) 11  5x
43) 2  33x
Solve the exponential growth/decay problem. Use the formula y  Aekt .
44) After 12 hours, half of a 16-gram sample of radioactive element is left. What is the approximate value of
? Assume is measured in hours. Round your answer to four decimal places.
45) For a certain strain of bacteria,
increase to 675 bacteria?
is 0.728 when is measured in days. How long will it take 10 bacteria to
Solve the continuously compounded interest problem. Use the formula A  Pert .
46) Carl plans to invest $500 at 8.25% interest, compounded continuously. How long will it take for his money
to triple? Round your answer to the nearest tenth of a year.
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