Let us now understand by an actual logarithm, a symbol of the form log a, in which a is any positive number, while b is any positive number > 1, and which denotes such a positive or negative number or zero, that when the “base” b is potentiated by it, the result will be the “logarithmand” a,—the actual logarithm therefore will always have a value and never more than one, and that value is negative, zero, or positive, according as the logarithmand is < 1, = 1, or > 1.