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  1. We use can logarithms to solve exponential equations: = b is x = log a bFor example, the solution of ex. 2 is x = log e 2. To find the value of this logarithm, we need to use a calculator. log e 2 = 0.6931.Note Logarithms were invented and used for solving exponential equations by the Scottish baron John Napi.

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  3. The aims of time series analysis are to describe and summarise time series data, fit low-dimensional models, and make forecasts. We write our real-valued series of observations as . . . , X−2, X−1, X0, X1, X2, . . ., a doubly infinite sequence of real-valued random variables indexed by Z.

  4. log(100) This usually means that the base is really 10. It is called a "common logarithm". Engineers love to use it. On a calculator it is the "log" button. It is how many times we need to use 10 in a multiplication, to get our desired number.

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