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  = -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