Learning Objectives:

__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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