Algebra 2: Exam #6 Study Guide
Name:________________________________Period:_____Score:_______/100
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
5) log k m  w
6) log3 x  2
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.
10)
log5 2m3 x 
11)
 6x 2 
3 
 5n 
log7 
12)
 my3 

  5n 2 


log 4 
Directions: Write each logarithmic expression as a single logarithm.
1
log 9 m  3log 9 w
13) 2
14)
1
4 log x  5 log k  log w
3
15) 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
16) log 20
17) log 0.4
18) log 25
Directions: Solve for x showing all your work. When necessary, round your answer to the nearest
ten thousandth. Circle your final answer.
19)
5
2 ln x  ln e  15
22) log 7 4x  23  18
6
25)
105x9  75
11
20) log5 125x
23)
 47
2 3x5  1611
26) 2 ln x  3ln 2  5
21)
log16 4 x 
5
16
24) 5ex  7  27
27) 4 x  7  25
28)
log2 .03125  x
31) log 25x   log 2  3
29) e4 x7  507
32)
34) log2 2x  2   log2 x  1  9
37 4 x1  1253
30) ln 1  2x   3
33)
92x5  911
Directions: Solve each problem showing all your work.
35) 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?
36) 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?
37) How long will you have to invest $500 if you earn 3.74% compounded continuously and you want
to double your money?