# Properties Or Rules Of Logarithms

These lessons are compiled to help Algebra students learn the properties or rules of logarithms.

#### Product Property

${\log _b}\left( {xy} \right) = {\log _b}x + {\log _b}y$

#### Quotient Property

${\log _b}\left( {\frac{x}{y}} \right) = {\log _b}x - {\log _b}y$

#### Power Property

${\log _b}\left( {{x^n}} \right) = n{\log _b}x$

#### Change Of Base Property

${\log _b}x = \frac{{{{\log }_a}x}}{{{{\log }_a}b}}$

### Properties Of Logarithms

This video explains three properties of logarithms and the Change of Base formula.

The product property is that the sum of two logarithms of the same base is equal to the log of the product of those two numbers.

The quotient property of logarithms is that the difference of two logarithms of the same base is equal to the logarithm of the quotient of those two numbers.

If you have the logarithm of a number that has an exponent that exponent can be taken out and multiplied times the logarithm to make it an equivalent expression.

The Change of Base formula is useful in determining values of logarithms with a base different than 10 .

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 