# Math

Some of the content of this guide was modeled after a guide originally created by the Openstax and has been adapted for the GPRC Learning Commons in October 2020. The graphs are generated using Desmos. This work is licensed under a Creative Commons BY 4.0 International License ## Defining Logarithms

##### The logarithmic function with base b is defined as: ##### 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, ##### We simplify this  logarithm using property 2): ##### 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: ##### Step 1) We use and then property 3): ##### Step 2) We use and then property 3): ##### Step 3) Finally, using property 4) we get: 