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Logarithm and Scientific Notation

1. Imagine that every single person in your contact list has the same number of people in their contact list as you. Write this total number of all the contacts in all the phones (ignore the fact that some may repeat) as an exponential. Next, evaluate this exponential.

2. Express the value you calculated in the first problem using scientific notation.

3. What would happen if each person added an extra contact. By what percentage would this change your answer? Would this percentage be smaller, larger or the same if someone started with a shorter list?

4. The exponential in number 1 and the value it comes out to can be written as an equality. Rewrite this equality using a logarithm.

5. For this last exercise we will take another number from your daily life. Let's calculate how big a cube you would need to hold 1 gallon of milk. If you were given that one gallon has 231 cubic inches, use roots to calculate how big each side of this cube would have to be to hold a gallon.

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The solution is 265 words in length.