Chapter 5

Lnx 3 3 ln x 5 ln 2x 3 3 ln 2x 6 log a c

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a)

Graph
the
function
N(t)
 
 
 
 
 
 
 
 
 
 
 
 b) Find
the
average
rate
of
change
of
the
population
over
the
time
period
 5 ≤ t ≤ 7
 
 
 
 
 
 
 
 
 
 
 
 
 c) 
Use
your
knowledge
about
the
exponential
function
to
compute
the
 Instantaneous
Rate
of
Change
of
the
population
at
the
instant
t
=
7
hours
 
 
 
 
 
 
 
 
 
 
 
 
 
 Logarithmic
Functions
(5.3)
 
 Recall
the
general
graph
of
the
exponential
function
 y = 2x .

This
function
passes
the
 horizontal
line
test.

Thus
it
is
one
to
one
and
has
an
inverse.
 
 Procedure
for
finding
the
inverse
of
f(x)
or
 f −1( x ) 
 
 In
this
case
 y = f ( x ) = 2x 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Definition:

The
logarithm
base
b
of
x,
denoted
 log b x ,

represents
the
exponent
to
 which
b
must
be
raised
to
yield
x.


 
 Another
words,

 
 
 
 
 
 
 
 This
relationship
allows
one
to
convert
logarithmic
equation
to
exponential
 equation
and
vice
versa.
 Ex:

Now
let’s
sketch
the
graphs
of
 y = log 3 x , y = logx and y = lnx on
the
same
set
 of
axes.

You
can
figure
out
th...
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This note was uploaded on 02/08/2011 for the course MATH 3 taught by Professor Staff during the Winter '08 term at UCSC.

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