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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