# Algebra Properties

**Published:** Jun 21, 2020

**Last updated:** Jun 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.

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## Associativity Property of Algebra

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

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## 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.

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## Additive Identity Property

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## Multiplicative Identity Property

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## Additive Inverse Property

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## Multiplicative Inverse Property

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## 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:

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## Quotient Rule

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

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## Power Rule

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

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## 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:

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## Base Switch Rule

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## Dennis O'Keeffe

Melbourne, Australia

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Algebra Properties

Introduction