


LogarithmsWhy Use Logarithms?Suppose we have a very efficient way of writing any number as powers of a fixed number, say 10: x = 10^{m} y = 10^{n} Then we can perform multiplication and division by using addition and subtraction (of exponents): xy = 10^{m+n} = 10^{m−n} A logarithm is just another name for an exponent with respect to a certain base such as 10.
The General LogarithmLet b > 0. If y = b^{x}, then we write log_{b}(y) = x or simply log_{b} y = x (read "log of y with base b") Note: log_{b} y is not defined for y ≤ 0 , as y = b^{x} > 0 for any x (as b > 0). ExampleExerciseFor this exercise, evaluate the logarithm, to the base shown, of the number.
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