 ## Tutoring on Using the Properties Logarithms

Learning Objectives:

#### Understand to use Properties of Logarithms.

Math Tutoring on Using the Properties of Logarithms

Following are the properties of logarithms:

Product Property:  The log of a product equals the sum of the logs.

1. logₐ (uv) = logₐ u + logₐ v        or         ln (uv) = ln u + ln v

Quotient Property: The log of a quotient equals the difference of the logs.

2. logₐ (u / v) = logₐ u - logₐ v       or         ln (u / v) = ln u - ln v

Power Property: The log of a power equals the product of power and the log

3. logₐ un = n logₐ u                     or         ln un = n ln u

Also few more properties on logarithms:

1.  logₐ1 = 0            since   a° = 1

2.  logₐa = 1            since   a¹ = 1

3.  logₐaᵐ = m        since   aᵐ = a

There is a change of base formula for converting between different bases.

logₐ x = ( logᵣ x ) / ( logᵣ a ) .

There is no need that either base 10 or base e be used.

logₐ x = ( log x ) / ( log a ) = ( ln x ) / ( ln a ).

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Hook Questions:

1. What is the base formula for converting between different bases?

2. What are the different properties of the logarithm?

3.  Explain power property of logarithms.

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