LOGS REVIEW WS
NAME ________________________
#1-4. Write as an exponential equation:
1.
log 4
1
 3
64
log x 3  2
2.
3.
ln148  5
4. log x  7
#5-7. Write as a logarithmic equation:
5. 13  169
6.
2
6x  3.6
7.
e3  20.1
#8-10. Expand using the properties of logs.
8.
9.
ln 2x 2 y
log
15 x
y
10.
log 2
z
x y
3
#11-13. Condense using the properties of logs.
11.
log8 5  log8 3
12.
1
log x  log 2
3
1
ln 3  4ln x  ln y
2
13.
#14-17. Solve the following equations
14.
82 x7  8x4
15.
22 x3  16
16.
4x 
1
256
17.
1
 
9
x 1
 27 2 x 4
#18-27. Evaluate the following
1
243
18.
log10000
19.
log 3
23.
ln e1.7
24.
log8 4
20.
log 25 5
21.
log9 1
22.
25.
eln 3
26.
log 4 32
27.
5log5 4
log 1 27
3
#28-30.
28.
Rewrite each using the change-of-base formula.
log 3 12
log 3 7
#31-36.
31.
34.
29.
log 1 x  2
32.
log 64 x 
35.
log x
3
37.
40.
ln 5
ln 8
1
2
1
 2
4
33.
1
log 2    x
4
36.
log 25 x 
3
2
Find each inverse function.
y  ln( x  3)  4
#40-42.
30.
Solve the following log equations.
log 4 x  3
#37-39.
log15
log 2
38.
y  log 2 x  1
39.
y  4x  3
41.
y  log 2 ( x  3)
42.
y  log 2 ( x  2)  4
Graph each function.
y  log 2 x
LOGS REVIEW WS ‒ ANSWERS
43 
1
64
2.
x2  3
3. e  148
6.
log6 3.6  x
7.
8. ln 2  2ln x  ln y
9.
1
log15  log x  log y
2
11. log8 15
12. log
14. 11
15.
18. 4
19. ‒5
23. 1.7
24.
2
3
25. 3
29.
log 2 15
30.
log8 5
‒2
1.
2.
5.
log13 169  2
3
28.
log 7 12
x
2
1
2
13.
10.
ln
3
x
4
33.
34. 9
35. 2
36. 125
38.
y  2 x 1
y
1
2
32. 8
y  e x 4  3
log2 z  3log2 x  log 2 y
16. ‒4
20.
39.
107  x
ln 20.1  3
31. 64
37.
4.
5
y  log 4 ( x  3)
17.
5
4
21. 0
22. 4
5
2
27. ‒3
26.