In an earlier post, I talked about adding numbers/quantities together with the sigma sum notation.
We had
In this post, the focus is on the multiplication case. Instead of having
The big Pi symbol above is used to represent a product of numbers.
Suppose you have the expression
In terms of product notation, this can be represented as:
The starting number is when k = 2 which would be just 2. Then you increase the index variable k by one each time you get the next number. When k is 3 you have the next number as 3. Continue this process until you have the upper limit of k = 10.
(The above example is an example of an ascending factorial. You can start the index at k = 1 instead of k = 2.)
Variables With Subscripts Case
Consider the case where you multiply the following:
The subscripts keep increasing by 1. The above can be represented in product notation as:
I have used a different index variable which is j. (You could use other common letters like i, or k.)
Exponent Laws
The following expression
can be expressed as n represents the number of twos in the product. In Pi product notation, the above can be represented as:
If you have something like
Logarithms
In this example, I use the natural logarithm where
One property of logarithms is where the logarithm of a product is the sum of the logarithms with separate components.
The general case for logartihms would be as follows:
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