 |
 |
 |
|
 |
|
 |
|
 |
|
 |
|
 |
 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
 |
|
|
|
Contents
Exponential & Logarithmic Function
Logarithmic Function
|
Logarithmic Functions
The logarithmic
function is the inverse function of the exponential function.
Proof:
Let y = f(x) = ex
ln y = ln ex
x = ln
y
power law
of logarithms
f-1 (x) = ln x
The idea of
finding inverse of a function is explained in our section on functions.
To obtain the graph
of the logarithmic function, we simply reflect the graph of y = ex
about the line y = x.
Properties of
the Logarithmic Graph
1. The x-intercept
is 1.
2. x = 0 is the
vertical asymptote.
3. The graph is
defined only for x > 0.
4. As x tends to
positive infinity, y tends to positive infinity.
5. As x tends to
positive zero, y tends to negative infinity.
6. The graph is an
increasing function.
|
