# Algebra Properties

June 21, 2020

## Resources

## Properties of Algebra

### Commutative Property of Algebra

Definition:

- involving the condition that a group of quantities connected by operators gives the same result whatever the order of the quantities involved, e.g. a × b = b × a.
- relating to or involving substitution or exchange.

### Associativity Property of Algebra

Grouping of more than two numbers to perform basic aritmetic operations of addition/multiplication does not affect the final result.

### Distributive Property of Algebra

The distributive property defines that the product of a single term and a sum or difference of two or more terms inside the bracket is same as multiplying each addend by the single term and then adding or subtracting the products.

### Additive Identity Property

### Multiplicative Identity Property

### Additive Inverse Property

### Multiplicative Inverse Property

## Logarithmic Properties

### Product Rule

The log of a product is equal to the sum of the log of the first base and the log of the second base:

### Quotient Rule

The log of a quotient is equal to the difference of the logs of the numerator and denominator:

### Power Rule

The log of a power is equal to the power times the log of the base:

### Change of Base Formula

The log of a new base is the log of the new base divided by the log of the old base in the new base:

### Base Switch Rule

### Related Articles

A personal blog on all things of interest. Written by **Dennis O'Keeffe**, Follow me on Twitter