Introduction to logarithm laws.

1. Don't forget ...
a logarithm is an exponent!
... if you do you may get mud on your face.
Pararescue by flickr user slagheap

2. Let's see 2^x
Then, sketch the graph of it's inverse ...

3. Sketch the
given function
AND it's inverse
on the graph.

4. Rewrite each table of values for the inverse of each function ...

5. The Anatomy Of A Power
exponent
3
2 = 8power
base
power
EXPONENTIAL FUNCTIONS
turn EXPONENTS into POWERS

6. a
b=c log b c = a
b is the base
b is the base
a is the exponent a is the (exponent) logarithm
c is the power c is the (power) argument
These functions are inverses of each other.
EXPONENTIAL FUNCTIONS LOGARITHMIC FUNCTIONS
turn EXPONENTS into POWERS turn POWERS into EXPONENTS

7. a
b=c log b c = a
b is the base
b is the base
a is the exponent a is the (exponent) logarithm
c is the power c is the (power) argument
A Logarithm is an Exponent
you're going to forget that

8. Graph the function
(a) Is there an asymptote? If so state its equation. If not, explain why not.
(b) State the domain.
(c) State the range.
(d) Is the function increasing or decreasing. Explain.

9. Simplify
.
The Product Law

10. Simplify
The Quotient Law

11. Simplify
The Power Law

12. 3
log2 8 = log2 2 =
In General ...
x
log5 5 = x
loga a = x
x
log7 49 =
loga a =

13. log 39
=9
3
In General ...
log ax
=x
log 710
a
=
7