Logarithms

1. Definition of Logarithms
   When and , for a positive number , the real number that satisfies is denoted as , and it is called the logarithm of to the base . In this case, is called the argument of .
   :
   
   
2. Properties of Logarithms
   When , , , and :
1. ,
4. (where is a real number)


3. Change of Base Formula
   When , , , , and :