For simplicity, we restrict our attention to common
logarithms, though any logarithm will work for these calculations. |
First, the definition. For any positive number X, the
logarithm of X, log(X), is the number making |
10log(X) = X |
true. That is, log(X) and 10X are inverses of
one another. For example, |
log(10) = 1 | because 101 = 10 |
log(100) = 2 | because 102 = 100 |
log(1) = 0 | because 100 = 1 |
log(17.5) = 1.24304 | because 101.24304 = 17.5 |
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By its design, the logarithm is a tool for extracting exponents. |
We will need to know three things about the logarithm. |
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