5) logarithms graphs

Exponential & Logarithmic functions
To explore the properties of exponential and logarithmic
functions and their graphs.
To understand the nature and behavior of exponential
growth and decay.

y = a x
,a > 1
Exponential growth
Asymptote:
y = 0
y- intercept:
(0, 1 )
We have already studied the graphs of
exponential functions.
y = a x
,0 < a <1
Exponential decay

x          f(x)
1       2
2       4
3       8
4       16
0       1
1      0.5
2        1
4        2
8        3
16      4
1        0
0.5     1
x            g(x)
Complete the tables:
Draw sketches of both graphs on the same grid.

The logarithm with base e is called "natural logarithm".
loge = ln
ln e =
ln 1 =
ln e2
=
Use your calculator to sketch the graph of
y = ln x

The natural logarithm function
ln e =
ln 1 =
ln e2
=

With your calculator draw the graphs of
y =log x , y = ln x and use the graph you drew for
y =log2x to describe the common features of
logarithms graphs.
• graph crosses the xaxis at (1,0)
• it only exist for x >0, the graph is to the right
of the yaxis
• log is negative for 0<x<1 and positive for x>1
• the yaxis is an asymptote to the curve

we1: Express each logarithm in its simplest form:
ln e5
=

we2: Find the value of x:
ln x = 0
ln x + 1 = 0
ln x = 1

http://www.youtube.com/watch?v=FQA2rkpBSY&feature=player_embedded#at=10

5) logarithms graphs

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5) logarithms graphs