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In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x. In the simplest case, the logarithm counts the number of occurrences of the same factor in repeated multiplication; e.g., since 1000 = 10?×?10?×?10 = 103, the "logarithm to base 10" of 1000 is 3. The logarithm of x to base b is denoted as logb , or without parentheses, logb x, or even without the explicit base, log x?if no confusion is possible.