Expert: Richard J. Raridon - 7/18/2010

Question
Part 1
Select the best answer from the choices provided. (Each question is worth one point)
1.   Simplify the logarithm:

log4 16
  4      2
  64      16
2.   Simplify the logarithm:

log7 49
  4      2
  8      1
3.   Simplify the logarithm:

log6 6
  6      36
  1      12
4.   Simplify the logarithm:

log2 1/8
  -4      0.25
  -3      4
5.   Simplify the logarithm:

log5 25
  25      5
  -5      2
6.   Simplify the logarithm:

log3 fifth root of 9
  
5
2
     
5
9
  
2
5
     
1
2
7.   Simplify the logarithm:

log1/3 27
  -3      9
  3      -9
8.   Simplify the logarithm:

log10 1
  -3      0
  -2      
-2
3
9.   Solve:

log6x = 3
  18      2
  54      216
10.   Solve:

logx64 = 6
  4      8
  16      2
11.   Solve:

logx7 = 1
  7      1
  0      17
12.   Solve:

logx2 = 0
  0      1
  no solution      -1
13.   Express the logarithm in terms of log2M and log2N:

log2(MN)4
  2(log2M + log2N)      8(log2M + log2N)
  4(log2M + log2N)      16(log2M + log2N)
14.   Express the logarithm in terms of log2M and log2N:

log2 the cube root of M2N
  3(2log2M + log2N)      1/3(2log2M + log2N)
  6(log2M + 1/2log2N)      2(log2M + 2log2N)
15.   Express the logarithm in terms of log2M and log2N:

log2 (M/N)7
  7(log2M + log2N)      14(log2M - log2N)
  14(log2M + log2N)      7(log2M - log2N)
16.   Express the logarithm in terms of log2M and log2N:

log2 1/MN
  - (log2M + log2N)      log21 (log2M + log2N)
  2(log2M + log2N)      2(log2M - log2N)
17.   If log10 9 = 0.95 and log10 2 = 0.3:

log10 36 =
  0.2708      1.2855
  1.5563      1.3423
18.   If log10 9 = 0.95 and log10 2 = 0.3:

log10 1/2000 =
  -3      -3.3010
  0.3010      -3.045
19.   Condense to a single log expression:

log10 x - 4log10 y
  log10 x/y4      log10 y4/x
  log10 xy/4      log10
20.   Condense to a single log expression:

log5 x - log5 y + 2
  log5 5x/y      log5 (x/y) + 2
  log5 2x/y      log5 5y/x
21.   Condense to a single log expression:
[1 - 5log3x]/2
  
  
1/2 - 5log3√    x
     
log3    

√3
(√x)5
  
  
5log√    x3
     
  
5log3√    x
22.   Simplify:

2log3 6 - log3 4
  3      6
  4      2
23.   Simplify:

log4 3 - log4 48
  16      -4
  -2      -16
24.   Solve the equation:

loga x = 3/2loga 9 + loga 2
  54      18
  27      36
25.   Solve the equation:

logb (x2 + 7) = 2/3logb 64
  9      3
  
Ö   23
     ±3
26.   Solve the equation:

loga (3x + 5) - loga (x - 5) = loga 8
  9      4.09
  8      3.54
27.   Find the value of the expression to three significant digits:

(10.6)10
  1.79 x 1010      179 x 1010
  17.9 x 1010      17.9 x 108
28.   Find the value of the expression to three significant digits:

The sixth root of 786
  131      3.04
  11.45      13.24
29.   Find the value of the expression to three significant digits:

log x = 1.96
  92.1      21.9
  91.2      19.2
30.   Find the value of the expression to three significant digits:

log3 x = 4.3
  112      113
  400      311
Part 2
Type the answer to the problem in the text box below each item. Be sure legibly show all work in your notebook. Remember to include any applicable units. If there is no solution, type "no solution". If there is not enough information present to solve the problem, type "not enough information". (Each question is worth two points)
31.   Solve:

122x = 1000
32.   Solve to three significant digits:

x2/3 = 50
33.   Solve:

(The fifth root of x) divided by 9, is equal to 7
34.   Solve to three significant digits:

The cube root of (4t plus 3) is equal to 8.15

Answer
You need to learn to use ^ for powers, such as x^2
1. 2
2. 2
3. 1
4. -3
5. 2
6. log3(9^1/5)
7. -3
8. 0
9. 216
10. 2
11. 7
12. no solution
17. 1.5563
18. -3.3010
27. (10.6)^10 = 1.79x10^10
28. 3.04
29. 91.2
30. 113
31. 8.197
32. 353
33. 9.924x10^8
34. 135