The function y = ax

1
The function y ax
2
The function y ax
y 3x
3
The function y ax
y 3x
y 2x
4
The function y ax
y 3x
y 2x
y 1.5x
5
The function y ax
y 3x
y (1/2)x
y 2x
y 1.5x
6
The function y ax
y 3x
y (1/3)x
y (1/2)x
y 2x
y 1.5x
7
The function y ax
y 3x
y (1/3)x
y (1/2)x
y 2x
y 1.5x
y (2/3)x
These are all exponential functions. They all
have powers of x. A power is also called an
EXPONENT
So, why dont we call them POWERFUL functions??
8
Using Exponential Graphs
y 10x
Find x when 10x 600 10x 400 10x
150
9
Logarithms

• Logs

log
10
The mysterious button on your calculator
log
What does it do?
11
Investigate this.
100 Log 0
101 Log 10
102 Log 100
103 Log 1000
104 Log 10000
12
What are logs?
exponent
value
base
13
What are logs?
exponent
base
value
14
In other words
means that
15
Earlier we used exponential graphs to estimate
answers to
Now we can use logs to find the exact answers!
Find x when 10x 600 10x 400 10x 150
16
Rewriting exponential equations as logarithms

• Rewrite these equations as logs
• 103 1000
• 54 625
• 210 1024

17
Important results to learn
For any base number.
18
Evaluating Logs

• Find the value of
• Log381
• Log40.25
• Log0.54
• Loga(a5)