Lesson Overview:

 

• -Evaluate the Log

• -Expanding and Condensing the Log

 

Part A: Evaluate the Log

First, we must understand that Log is an exponent.

Now we will evaluate the Log by forming equivalent exponential equations. 

 

 

 

 

 

 

 

 

 

Because Log is an exponent we know that we can use the equations on the left to form an equivalent exponential equation on the right.

 

Part B: Expanding and Condensing Log

Before we start, we have to know the rules of exponents and logarithm

 

 

 

 

 

 

 

 

 

 

Keeping those in mind, we can start expanding/condensing

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In this example, we start expanding by distributing the log to every term and translate multiplication to addition. Then we bring any exponents to the front of the log finally we box our answer.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Here, we must condense the log and we start doing that by moving up any numbers in the front of the log to exponents. Next, we change any subtraction among logs into division, moving them to the denominator. Finally, we finish by condense the log into one fraction with a log base of 5 and box our answer.

SAT Testing of Rational Expressions and Equations

 

 

 

 

 

 

 

 

 

 

 

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Real World Application

 

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The Richter Scale uses an exponential graph to calculate and represent the magnitude and classify the level of earthquakes.

 

Conclusion:

After this lesson, students should be able to predict the shape of rational functions by using sign diagrams. After their predictions, they should be able to graph the functions on graph paper by following the basic rules learned. These skills can be used to predict the graph of rational functions when given the equation as shown in the example above.