1. Logarithmic Functions
Let a be a positive number with a ≠ 1. The logarithmic function with base a, denoted by loga, is defined by
is the exponent to which the base a must be raised to give x.
Ex 1: Rewrite in exponential form
a b.

2. Ex 2: Rewrite in logarithmic form
a b.
Ex 3: Evaluate a. b. c.

3. Properties of Logarithms
We raise a to the 0 power to get 1.
We raise a to the 1 power to get a.
We raise a to the x power to get ax.
loga x is the power to which a must be raised to get x.

4. Ex 4: Evaluate
a. b.
c. d.

5. Ex 5: Graph by graphing

6. Ex 6: Graph and

7. Ex 7: Find the domain of
and sketch the function. D:

8. Ex 8: Find the domain of
and sketch the function. D:

9. The logarithm with base 10 is called the common
The logarithm with base 10 is called the common logarithm and is denoted by omitting the base:
Ex 9: Use a calculator to evaluate.
a. b.

10. Ex 10: The perception of loudness B (in decibels)
Ex 10: The perception of loudness B (in decibels) of a sound with physical intensity I is given by
where I0 is the physical intensity of a barely audible sound. Find the decibel level of a sound whose physical intensity I is 100 times that of I0.

11. Properties of Natural Logarithms
The logarithm with base e is called the natural logarithm and is denoted by ln:
Properties of Natural Logarithms
We raise e to the 0 power to get 1.
We raise e to the 1 power to get a.
We raise e to the x power to get ex.
ln x is the power to which e must be raised to get x.

12. Ex 12: Find the domain of the function
Ex 11: Evaluate the following.
a. b. c.
Ex 12: Find the domain of the function D:

13. Assignment (#30) S 5.2: pg
#2,3,10,11,14,24,32,33,36,
39-43,58-60