 ## Tutoring on Evaluating Logarithmic Expressions

Learning Objectives:

#### Understand to Evaluate Logarithmic Expressions

Math Tutoring on Evaluating Logarithmic Expressions

To evaluate Logarithmic Expressions we need to know the properties of logarithmic functions in math tutoring. 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 of 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 ).

So, during math tutoring when evaluating logarithms all that we are really asking is what exponent did we put onto the base to get the number in the logarithm?

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Hook questions:

1. What is the parent function of a logarithmic equation?

2. How do you graph a natural log?

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

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