3.3: Properties of Logarithms

Although common logs and natural logs are the most frequently used, you may occasionally need to evaluate logarithms to other bases. To do this, you can use change-of-base formulas.

Change-of-Base Formulas

Base b

Base 10

Base e

Properties of Logarithms

Let a be a positive number such that a  1, and let n be a real number. If u and v  are positive real numbers, the following properties are true.

1.                        4.

2.                            5. 

3.                                       6.