Algebra 2: Logarithm Exam Study Guide
Name:________________________________Period:_____
Directions: Rewrite each exponential equation as a logarithmic equation.
3
1) 4  64
2) 10
2.57
x
x
2) 3  5
Directions: Rewrite each logarithmic equation as an exponential equation.
4) log5 125  3
6) log3 x  2
5) log k m  w
Directions: Rewrite each logarithmic expression in base ten using the change of base
formula. When possible, evaluate the expression. SHOW ALL YOUR WORK.
7) log 3 15
8) log 3 w
9) log 4 512
Directions: Expand each logarithm.
𝑚
10) log 𝑛
11)
log 5 2m3 x 
 6x 2 
12) log7  3 
 5n 
Directions: Write each logarithmic expression as a single logarithm.
13)
1
2
log 9 𝑚 + 3 log 9 𝑤
14) 2log x  log6  log m
Directions: Use the properties of logs to find the approximations of the following, given
log 2  0.3 and log 5  0.7
15) log 20
16) log 0.4
17) log 25
Directions: Solve for x showing all your work. When necessary, round your answer
to the nearest ten thousandth. Circle your final answer.
18)
21)
2 ln x  ln e5  15
2 3x5  1611
24) 2ln x  3ln2  5
27)
37 4 x1  1253
11
19) log 5 125x  47
20) log 7 4x  23  18
22) 5e x  7  27
23)
25)
log 2 .03125  x
6
105x9  75
26) log 25x   log 2  3
28) log2 2x  2   log2 x  1  9
Directions: Solve each problem showing all your work.
29) Henry invested $1200 in a 6 year CD at a 5.25% interest rate. The interest is
compounded monthly. How much money will Henry have when his CD matures?
30) Katherine invests $1000 in a 5 year CD that compounds interest continuously. She
was thrilled to lock in at a 5.73% interest rate. How much money will Katherine have
when her CD matures?
31) How long will you have to invest $500 if you earn 3.74% compounded continuously
and you want to double your money?
Benchmark #3 Review Problems
Directions: Simplify the radical expression. Show all your work.
32)
12
45
33)
4
81
7
34)
3
27 w6
125 x15
35)
5
36) (251/ 2 )(163/ 4 )
2−√6
37)
 25x
1/ 3
m3/ 2 y 2/ 3 
1/ 2
38) 4√50 + 6√72
Directions: Describe the transformation of f represented by g. Then graph each
function.
40) 𝑓(𝑥) = 3√𝑥, 𝑔(𝑥) = 3√𝑥 − 2 + 1
39) 𝑓(𝑥) = √𝑥, 𝑔(𝑥) = −√𝑥 + 1
-10
12
12
10
10
8
8
6
6
4
4
2
2
-5
5
10
-10
-5
5
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
-12
-12
Directions: Solve each equation and check your answer(s).
3
41) √3𝑥 + 1 = −5
42) 2 + √3𝑥 − 2 = 6
Directions: For the following problems, let 𝑓(𝑥) = 2𝑥 2, 𝑔(𝑥) = 3𝑥 − 1 and ℎ(𝑥) = 4𝑥 − 2.
43) 𝑓(ℎ(2))
44) (𝑓 ∘ 𝑔)(3)
45) ℎ(𝑓(𝑥))
10