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# Applications of Logarithms

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4) For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, , let r = 8%, P = 1, and n = 1 and give the coordinates (t,A) for the points where t = 0, 1, 2, 3, 4.
a) Show coordinates in this space.

Show work in this space.

b) Show graph here.

5) Logarithms:
a) Using a calculator, find log 1000 where log means log to the base of 10.

b) Most calculators have 2 different logs on them: log, which is base 10, and ln, which is base e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer, 0 and 1. When a computer scientist needs a logarithm, he needs a log to base 2 which is not on any calculator. To find the log of a number to any base, we can use a conversion formula as shown here:

Using this formula, find .