The log rules

Log Rules

1. Block 3
The Log Rules

2. What is to be learned?
•The three log rules and how to apply them
•(also two log mini rules)

3. a
x
X a
y
= a
x + y
let P = a
x
and Q = a
y
PQ = a
x + y
logPQ
a = x + y
logP
a
= xlogQ
a
= y
= log
a
P + log
a
Q
for log addition you multiply
logPQ
a

4. log
a
12

+ log
a
4 =
log
6
10

+ log
6
8 =
log
a
48
log
6
80
log
4
5

+ log
5
4

=cannot simplify
base numbers must be the same

5. log
a
3 + log
a
4 =
log
a
12 – log
a
4 =
log
6
16

– log
6
8 =
log
a
3
log
6
2
for log subtraction you divide
log
a
12

6. Two Mini Rules
log
10
10 = x
10 = 10
x
x = 1
log
10
10 = 1
log
a
a = 1
Translating

7. Mini Rule 2
log
10
1 = x
1 = 10
x
x = 0
log
10
1 = 0
log
a
1 = 0
Translating

8. Neat Wee Rule
log
10
1000 = x
1000 = 10
x
x = 3
log
10
1000 = log
10
10
3

log
10
10
3
= 3
= 3 X 1
= 3log
10
10
log
1010
3
=3log
1010
log
a
x
y
Translating

9. Using Neat Wee Rule (and the others)
2log
4
3 + log
4
2
log
4
3
2
+ log
4
2
log
4
9 + log
4
2
log
4
18

10. log
4
8 – 3log
4
2
log
4
8 – log
4
2
3

log
4
8 – log
4
8
log
4
1
0
Using Neat Wee Rule (and the others)

11. Log Rules
Addition
log
a
x

+ log
a
y = log
a
xy
Subtraction
log
a
x

– log
a
y = log
a
x
/
y
Neat Wee
log
a
x
y
= ylog
a
x

12. Log “Mini” Rules
log
a
a = 1
log
a
1 = 0
log
4
6 + log
4
2 – log
4
3
= log
4
12 – log
4
3
= log
44
= 1

13. 2log
6
4

– log
6
16
= log
6
4
2
– log
6
16
= log
6
16 – log
6
16
= log
6
1
=0

14. 3log
4
2 + log
4
3 – log
4
6
log
4
2
3
+ log
4
3 – log
4
6
log
4
8 + log
4
3 – log
4
6
log
4
24 – log
4
6
log
4
4
Key Question
1