Defining Logarithms
The logarithmic function with base b is defined as:
where x is called the argument of the logarithm and y is the value of the logarithm. The base of the logarithm, b, is always a positive number. One can use a calculator to find the value of a logarithmic function.
Example: What is the value of 
?
The base of the logarithm is 9 and the argument is 4. We can use a calculator to find the value of this logarithm:
Properties of Logarithms.
1)The logarithm of a product is the sum of the logarithms:
2) The logarithm of a division is the difference of the logarithms:
3) The logarithm of a power:
4) For any base b,
5) For any base b,
Example: Use the logarithmic properties to simplify 
We simplify this logarithm using property 2):
Example: Use the logarithmic properties to simplify 
Step 1) We use property 1) to combine the first two logarithms:
Step 2) We use property 2) to combine the two logarithms
Step 3) Using property 4) we get:
Example: Use the logarithmic properties to simplify
Step 1) We use 
and then property 3):
Step 2) We use 
and then property 3):
Step 3) Finally, using property 4) we get:
