Don't forget ...

a logarithm is an exponent!

... if you do you may get mud on your face.

Pararescue by flickr user slagheap

Then, sketch the graph of it's inverse ...

Let's see 2^x

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

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

23

= 8base

exponent

powerpower

The Anatomy Of A Power

EXPONENTIAL FUNCTIONS turn EXPONENTS into POWERS

b ca= logbc = 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

LOGARITHMIC FUNCTIONS turn POWERS into EXPONENTS

EXPONENTIAL FUNCTIONS turn EXPONENTS into POWERS

These functions are inverses of each other.

b ca= logbc = 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 Exponentyou're going to forget that

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.

Simplify

The Product Law

.

Simplify

The Quotient Law

Simplify

The Power Law

log 22

3 =log 82

=

log 55

x =log a

a

x =

In General ...

x

log 497

x=

log aa =

7 7log=

10

3 3log=

99

In General ...

a alog=

xx