Logarithmic Expressions
Using the Transformation Table for Simplifying Logarithms
Download Transformations[PDF] A good way to get used to the transformations is to find an example use of each transformation in the table. Print the transformation table and use the second column that has been provided for this purpose. Your textbook should provide you with examples. If not use the problem sets mentioned below in the various sections.
Numeric Problems [problem set = logps]
To use SMG for all problems involving simplifying loagarithms, download a PDF document.
Numeric problems provide a concrete introduction to using the properties of logarithms. Simplify the following expression involving logarithms. The following is a typical example of the use of logarithmic properties to simplify an expression.
Example
| The original problem appears on the right.
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| Press F4.
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| Press 1. |
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Press <ENTER> to simplify.
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Next, download a set of examples that contains two parts.[Download examples [PDF].] The first part consists of problems with a possible solution of SMG steps for each problem; the second part consists of problems without any type of solution or hints.Use the SMG problem set logps to work these examples on SMG without entering the problem yourself.
Problems Containing Variables [problem set = logps]
Example
| Original problem |
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| Press F4. You could choose 2, but let's put the first term in the order found in the property.
Press 1.
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| Press F4.
Press 1.
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| Press F4.
Press 2.
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Expanding Logarithmic Expressions [problem set = logexpps]
To use SMG to practice expanding expressions involving logarithms, download a PDF document. Note that no transformation table is provided. The primary transformations correspond to using 'simplify logarithm' transformations in reverse.
Entering New Problems (logarithmic expressions)
The easiest way to enter your own problem is to edit an existing problem of the same type. If the current problem is a Simplify Log & Exponential problem, press F2:2 to get the screen below. Make your changes and press <ENTER>.
To enter a new Simplify Log & Exponential problem, press F2:1, press F1:5 [not necessary if last problem created was the same type. Check the dialog’s title.], and type your expression. Press <ENTER> to complete the process.
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TIPS:
- When entering the product of two variables, say x and y, be sure to use * between them to indicate multiplication. SMG will treat xy as a single variable.
- You must type log for common logs (i.e. there is no special key)..
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Sub-expression Selection
- Selecting parts of logarithmic expressions gives you additional control over what you can do. See Example1. When a successful problem solver simplifies logarithmic expressions, she often thinks something like “Let’s apply the sum of two logs to the first two logs.” Let’s see how to do this with SMG by following an example.
Example: 
Press F3 [selects the first log].
Hold down shift and press right arrow [the sum of the first two logs is selected.]
Press F4 and choose 
- 1. Draw a tree structure for
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2. How do you select x?
3. Now, how do you select the 2?
4. Can you select log? Explain your answer.
5. Draw a tree structure for 
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6. How do you select the 3.
Strategy Session
- What is the goal of simplifying logarithmic expressions? Be specific and give an example.
- Look through the solutions to the worked out examples. What patterns do you see?
- How can seeing the pattern help you learn to solve these problems?
Alternative Questions
- Instead of downloading the transformations we provide, work through the examples and construct a collection of transformations that are useful for solving simplify problems and another for solving expand problems. Add these collections to your notebook. Clarify any questions you have by incuding useful examples.
Resources
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