Log Graphs

1. Block 3
Tricky log Graphs

2. What is to be learned?
• How to draw and recognise nasty log
graphs

3. Previously y = log4x
y = 4x
y = x
y = log4x
1
1

4. y = log4x
y = log4x
1
(4, 1)
( , 0)
x y
y = log41
y = 0
y = log44
y = 1
x = 1 x = 4
(1 , 0) (4 , 1)
Mini log rules are very helpful

5. Draw y = 4 log5x
sub x = 1 and
x = 5
x=1 y = 4log51
= 4 X 0 (1 , 0)
x=5 y =4 log55
= 0
(5 , 4)= 4= 4 X 1
(5, 4)
(1, 0)
y = 4 log5x

6. Draw y = 6 log7x
sub x = 1 and
x = 7
x=1 y = 6log71
= 6 X 0 (1 , 0)
x=7 y =6 log77
= 0
(7 , 6)= 6= 6 X 1
(7, 6)
(1, 0)
y = 6 log7x

7. Draw y = 2 log3(x – 1)
sub x = 2 and x = 4
x=2 y = 2log3(2 – 1)
= 2 X log31
(2 , 0)
x=4 y = 2log3(4 – 1)
= 2 X 0
(4 , 2)= 2 X 1
= 2 X log33
(4, 2)
(2, 0)
y = 2 log3 (x – 1)
want to equal 1 and 3
= 0
= 2

8. Sketching Nasty Log Graphs
Tactics
Find 2 points using mini log rules
i.e. chose x values to make
loga1 and
logaa

9. Draw y = 5log4(x – 2)
sub x = 3 and x = 6
x = 3 y = 5log4(3 – 2)
= 5 X log41
(3 , 0)
x = 6 y = 5log4(6 – 2)
= 5 X 0
(6 , 5)= 5 X 1
= 5 X log44
(6, 5)
(3, 0)
y = 5 log4 (x – 2)
want to equal 1 and 4
= 0
= 5

10. Draw y = 6 log3(x + 2)
sub x = -1 and x = 1
x=-1 y = 6log3(-1 + 2)
= 6 X log31
(-1 , 0)
x=1 y = 6log3(1 + 2)
= 6 X 0
(1 , 6)= 6 X 1
= 6 X log33
(1, 6)
(-1, 0)
y = 6 log3 (x + 2)
want to equal 1 and 3
= 0
= 6
Key Question

11. Identifying Log Graphs
(6, 7)
(2, 0)
Type y = a log5 (x + b)
?

12. Identifying Log Graphs
(6, 7)
(2, 0)
Type y = a log5 (x + b)
x y
x = 2, y = 0
→ 0 = a log5 (2 + b)
This one first!

13. Identifying Log Graphs
(6, 7)
(2, 0)
Type y = a log5 (x + b)
x y
x = 2, y = 0
→ 0 = a log5 (2 + b)
must equal 1
b = -1

y = a log5 (x – 1)
x y
x = 6, y = 7
7 = a log5 (6 – 1)

14. Identifying Log Graphs
Type y = a log5 (x + b)
x = 2, y = 0
→ 0 = a log5 (2 + b)
must equal 1
b = -1

y = a log5 (x – 1)
x = 6, y = 7
7 = a log5 (6 – 1)
7 = a log5 (5) 1
7 = a
y = 7 log5 (x – 1)

15. Identifying Log Graphs
(2, 3)
(-1, 0)
Type y = a log4 (x + b)
x y
x = -1, y = 0
→ 0 = a log4 (-1 + b)

16. Identifying Log Graphs
Type y = a log4 (x + b)
x = -1, y = 0
→ 0 = a log4 (-1 + b)
must equal 1
b = 2

y = a log4 (x + 2)
x y
x = 2, y = 3
3 = a log4(2 + 2)
(2, 3)
(-1, 0)
x y

17. Identifying Log Graphs
Type y = a log4 (x + b)
x = -1, y = 0
→ 0 = a log4 (-1 + b)
must equal 1
b = 2

y = a log4 (x + 2)
x = 2, y = 3
3 = a log4 (2 + 2)
3 = a log4 (4) 1
3 = a
y = 3 log4 (x + 2)

18. Identifying Log Graphs
Type y = a log5 (x + b)
Need to find a and b
mini log rules are vital again

19. This one first!
(6, 4)
(4, 0)
Type y = a log3 (x + b)
x y
x = 4, y = 0
→ 0 = a log3 (4 + b)
must equal 1
→ b = -3

y = a log3 (x – 3)
x y
x = 6, y = 4
4 = a log3 (6 – 3)
4 = a log3 3 1

20. Type y = a log3 (x + b)
x = 4, y = 0
→ 0 = a log3 (4 + b)
must equal 1
→ b = -3

y = a log3 (x – 3)
x = 6, y = 4
4 = a log3 (6 – 3)
4 = a log3 3 1
4 = a
y = 4 log3 (x – 3)
*
*
* Mini Log Rules

21. (6, 2)
(2, 0)
Type y = a log5 (x + b)
x y
x = 2, y = 0
→ 0 = a log5 (2 + b)
must equal 1
→ b = -1

y = a log5 (x – 1)
x y
x = 6, y = 2
2 = a log5 (6 – 1)
2 = a log5 5 1
2 = a
y = 2 log5 (x – 1)
Key Question

22. (12, 15)
(5, 0)
Type y = a log2 (x + b)Nastier!
y = 5 log2 (x – 4)
(7, 8)
(-1, 0)
Type y = a log3 (x + b)
y = 4 log3 (x + 2)
1.
2.