The function y = ax
The function y = ax
y = 3x
y
x
The function y = ax
y = 3x
y
y = 2x
x
The function y = ax
y = 3x
y
y = 2x
y = 1.5x
x
The function y = ax
y = 3x
y
y = (1/2)x
y = 2x
y = 1.5x
x
The function y = ax
y = (1/3)x
y = 3x
y
y = (1/2)x
y = 2x
y = 1.5x
x
The function y = ax
y = (1/3)x
y = 3x
y
y = (1/2)x
y = 2x
y = (2/3)x
y = 1.5x
x
These are all exponential functions. They all have powers of x.
A power is also called an EXPONENT
So, why don’t we call them POWERFUL functions……??
Using Exponential Graphs
y = 10x
y
Find x when
10x = 600
10x = 400
10x = 150
x
Logarithms
log
Logs
The mysterious button on your
calculator…
log
What does it do?
Investigate this….
100 =
Log 0 =
101 =
Log 10 =
102 =
Log 100 =
103 =
Log 1000 =
104 =
Log 10000 =
What are logs?
exponent
10  1000
3
base
value
What are logs?
exponent
10  1000
3
value
base
log 10 1000  3
base
value
exponent
In other words…
log a n  x
means that
a n
x
log a n  x
a n
x
Earlier we used exponential graphs to estimate answers to… Now we can use
y
logs to find the
exact answers!
Find x when
10x = 600
10x = 400
10x = 150
x
Rewriting exponential equations
as logarithms
Rewrite these equations as logs:
1. 103 = 1000
2. 54 = 625
3. 210 = 1024
log a n  x
a n
x
Important results to learn
For any base number….
log a 1  0 (a  0)
log a a  1
a  0 
Evaluating Logs
Find the value of:
1) Log381
2) Log40.25
3) Log0.54
4) Loga(a5)