Exponential and logarithmic conversions
NAME________________________ HOUR________
Today we are going to learn another way to write an exponent. The conversion is as follows:
ab=c can also be written logac=b
This is read “log base ‘a’ of ‘c’ equals ‘b’”
(THIS DOES NOT MEAN THAT ‘A’ IS RAISED TO THE POWER ‘C’!!)
Convert the following exponential equation into a logarithmic equation.
1.
43=64
2.
172=289
Convert each logarithmic equation into an exponential equation
.
4.
Log39=2
5.
Log8512=3
3.
81(1/4)=3
6.
Log366=1/2
Convert the following exponential equation into a logarithmic equation.
7.
63=216
8.
94=6561
9.
73=343
10.
153=3375
11.
37=2187
12.
7-2=1/49
13.
3-2=1/9
14.
(¼)2=1/16
15.
(1/3)-3=27
16.
81(1/2)=9
17.
144(1/2)=12
18.
7776(1/5)=6
Convert each logarithmic equation into an exponential equation.
19. Log28=3
20. Log72401=4
21. Log101000=3
22.
Log5125=3
23.
Log1000010=¼
24.
Log12966= ¼
25.
Log16913= ½
26.
Log265536=16
27.
Log1/636=-2
28.
Log1/273=-1/3
29.
Log41/64=3
30.
Log1/647=-1/2
Bonus: Which of the problems was incorrect?
Answers:
1.
Log464=3
2.
Log17289=2
6.
361/2=6
7.
Log6216=3
11. Log32187=7
12. Log71/49=-2
16. Log819=1/2
17. Log14412= ½
21. 103=1000
22. 53=125
26. 216=65536
27. 1/6-2=36
Bonus the last one, what was the mistake?
3.
8.
13.
18.
23.
28.
Log813= ¼
Log96561=4
Log31/9=-2
Log77766=1/5
10000(1/4)=10
1/27-1/3=3
4.
9.
14.
19.
24.
29.
32=9
Log7343=3
Log¼1/16=2
23=8
12961/4=6
4-1/3=1/64
5.
10.
15.
20.
25.
30.
83=512
Log153375=3
Log1/327=-3
74=2401
169(1/2)=13
1/64-1/2=7