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In this lesson, we will discuss at great length the logarithm laws that are used in all branches of math, science, and engineering. First, we will write down these log rules. Next we will construct a logical step by step proof of each logarithm law. At the end of the lesson, you will understand why, for example, addition of logarithms can be written as a multiplication. These laws of logs are used in higher math courses such as calculus, differential equations, and beyond because they lay the foundation for more complex problems.