# Come up with at least three different abbreviations for logarithms with different bases. For each one, explain why you chose the particular abbreviation, and evaluate the logarithm of a number with it.

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In the text field below, please provide your response to the following discussion prompt in 250-500 words. Then save the file as either .doc or .docx format, and upload the document into the Upload Area for Discussion 4:

Prompt 1:

Find an example of a graph of a polynomial function or rational function. Write the function down. Imagine you are traveling along the graph of the function from left to right. Describe your journey. Include details such as when you are going up or down, when you reach either a high point or a low point, when you cross the x- and y-axes, and any numbers you see on the axes.

Example: I approach the function . I come in from the left, way down low. The graph has a steep incline as I move to the right. I cross the x-axis at about . I keep going up until I hit a peak at a y coordinate of about 2.1. My altitude decreases as I continue following the graph to the right…

Prompt 2:

Find an example problem of compound interest or continuous compound interest. Read through the entire example and the solution. Using the numbers in the solution and the original problem, write a summary of the application scenario. Do not write this as a question. Rather, write this as though you had witnessed the event.

Example: I’ve got a thousand bucks and I’m ready to invest. I find a nice interest rate of 6.6%, compounded monthly. I talk the banker into compounding that money continuously…

Prompt 3:

Logarithms with base 10 are abbreviated “log,” and do not need to show the base 10 (). Logarithms with the natural base e are abbreviated “ln,” short for the Latin phrase “logarithmus naturali” (natural logarithm). Come up with at least three different abbreviations for logarithms with different bases. For each one, explain why you chose the particular abbreviation, and evaluate the logarithm of a number with it.

Example:

Today I introduce the “lz.” The lz is a logarithm of base 2. Its abbreviation lz comes from the German phrase “Logarithmus von zwei“ (logarithm of 2). Evaluate lz(x) just as though you are evaluating . For example, , because .