1. Write the equivalent logarithmic statement:
a. 53 = 125 | b. 34 = 81 | c. 23 = 8 |
d. 63 = 216 | e. 5-1 = | f. 1000 = 103 |
2. Write the equivalent index statement:
a. log 264 = 6 | b. log 3243 =5 | c. log 2 = -3 |
d. log 39 =2 | e. log 25125 = 1.5 | f. log 3 = -1 |
3. Calculate the following:
a. log 10 100
b. log 9 3
c. log 625125
d. log 16 32
e. log 0.1 10
4. Solve the following equations for x:
a. log 2 x = 6
b. log 3 x = 4
c. log x 3 = 1
d. log 3 27 = x + 2
e. log 5 25 = 3x + 1
5. Write as the log of a single number:
a. log 6 + log 5 | b. log 21 − log 7 | c. log 12 − log 2 + log 6 |
d. log 54 − (log 9 + log 6) | e. 2log 6 + 5log 2 | f. 3log 5 + 3log 2 − log 10 |
g. 2log 10 + log 25 − 3log 5 | h. log 64 + log 27 | i. log a + 3log b − 2log c |
6. Evaluate:
a. 2log 66
b. log 216 + log 2 4
7. Solve the following index equations:
a. 2x = 128 | b. 2x+1 = 32 | c. 9x = 3 | d. 64x = 32 |
8. Solve the following index equations (give the answers to 3 decimal places):
a. 10x = 9 | b. 3x = 4 |
c. 42x = 5x+2 | d. 3.64x + 5 = 2.92x + 13 |