|
A logarithm is an
exponent.
|
As this example shows, 3 is the
exponent to which the
base 2 must be raised to create the answer
of 8, or 23
= 8. In general terms:
|
(where x > 0 and
b is a positive constant
not equal to 1) |
|
|
BASE 10:
Logarithms with base 10 are called
common logarithms.
When the base is not indicated, base 10 is implied.
The log key on the
graphing calculator will calculate the
common (or base 10) logarithm.
2nd log
will calculate the antilogarithm or
10x
|
 |
OTHER BASES:
To enter a logarithm
with a different base on the graphing calculator, use the Change of Base
Formula:
|
 
|
BASE e:
Logarithms with base e
are called natural logarithms.
Natural logarithms are denoted by
ln.
On the graphing calculator, the base e logarithm is the
ln key.
|
|
|
e
2.71828183 |
|
|
|
When working with logarithms on your graphing calculator,
you must
remember the "Change of Base Formula":
|
|
Remember, the notation:
log x is with respect to base 10
ln x is with respect to base e |
Examples:
1. Evaluate:
 |
|
2. Evaluate:
ln 2; ln 1; ln e
|
|
3. Evaluate:
 |
|
4. Sketch the graph of
 |
 |
5. Use a graph to support the conclusion
that the inverse of
 is
 .
A function composed with its inverse creates the
identity line y = x. Showing that the
composition of these two functions is the identity line shows
that these functions are inverses of one another. Note the
bubble animation set for Y4 to show that the linear lines
in Y3 and Y4
are equivalent.
|
 |
6. Solve graphically:
Method 2:
This problem can also be solved by setting the
equation equal to 0 and finding the x-intercepts, or
zeros (2nd CALC, #2), of the function.
 |
Method 1:
The window must be
adjusted to show a sufficient amount of the x-axis to locate the
intersection point (2nd CALC, #5). The answer is x = 32.
 |
7. Using your graphing calculator,
determine which of the following statements are
true.
|
a.) T b.) F c.) F
d.) T e.) F f.) T |
|
Solution for part a:
(TRUE)
Place the left side of the equation in Y1 and the
right side in Y2. Turn on the "bubble
animation" to the left of the Y2. This
will allow you to see the bubble floating over the graph when
the equation is true. Parts b - f are solved in a similar
manner.
 |
|
